The hadith you've mentioned is not at all quoted in any of the hadith compilation which are present on sunnah.com except with a hadith that starts similarly in Jami' at-Tirmdihi:
Narrated 'Abdullah bin Mas'ud:
that the Prophet (ﷺ) said: "A man among the inhabitants of Paradise will appear before you." So Abu Bakr appeared. Then he said: "A man among the inhabitants of Paradise will appear before you." So 'Umar appeared.
So the hadith you are looking for is neither quoted in both Sahih books, nor in the Sunan of Abi Dawod, ibn Majah, an-Nassa-i, nor Jami' at-Tirmdihi, nor in A_Shamail al-Muhamamdiya, nor in Riyadh as-Saliheen, nor al-Muwatta'.
Nevertheless the hadith is famous because it appears in one of the biggest hadith collections: Musnad al-Imam Ahmad on the authorithy of Anas ibn Malik:
حَدَّثَنَا عَبْدُ الرَّزَّاقِ حَدَّثَنَا مَعْمَرٌ عَنِ الزُّهْرِيِّ قَالَ أَخْبَرَنِي أَنَسُ بْنُ مَالِكٍ رضي الله عنه قَالَ : كُنَّا جُلُوسًا مَعَ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ فَقَالَ : ( يَطْلُعُ عَلَيْكُمْ الْآنَ رَجُلٌ مِنْ أَهْلِ الْجَنَّةِ ) فَطَلَعَ رَجُلٌ مِنْ الْأَنْصَارِ تَنْطِفُ لِحْيَتُهُ مِنْ وُضُوئِهِ قَدْ تَعَلَّقَ نَعْلَيْهِ فِي يَدِهِ الشِّمَالِ ، فَلَمَّا كَانَ الْغَدُ قَالَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ مِثْلَ ذَلِكَ ، فَطَلَعَ ذَلِكَ الرَّجُلُ مِثْلَ الْمَرَّةِ الْأُولَى ، فَلَمَّا كَانَ الْيَوْمُ الثَّالِثُ قَالَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ مِثْلَ مَقَالَتِهِ أَيْضًا فَطَلَعَ ذَلِكَ الرَّجُلُ عَلَى مِثْلِ حَالِهِ الْأُولَى ، فَلَمَّا قَامَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ تَبِعَهُ عَبْدُ اللَّهِ بْنُ عَمْرِو بْنِ الْعَاصِ فَقَالَ : إِنِّي لَاحَيْتُ أَبِي فَأَقْسَمْتُ أَنْ لَا أَدْخُلَ عَلَيْهِ ثَلَاثًا ، فَإِنْ رَأَيْتَ أَنْ تُؤْوِيَنِي إِلَيْكَ حَتَّى تَمْضِيَ فَعَلْتَ . قَالَ نَعَمْ قَالَ أَنَسٌ : وَكَانَ عَبْدُ اللَّهِ يُحَدِّثُ أَنَّهُ بَاتَ مَعَهُ تِلْكَ اللَّيَالِي الثَّلَاثَ فَلَمْ يَرَهُ يَقُومُ مِنْ اللَّيْلِ شَيْئًا ، غَيْرَ أَنَّهُ إِذَا تَعَارَّ وَتَقَلَّبَ عَلَى فِرَاشِهِ ذَكَرَ اللَّهَ عَزَّ وَجَلَّ وَكَبَّرَ حَتَّى يَقُومَ لِصَلَاةِ الْفَجْرِ . قَالَ عَبْدُ اللَّهِ : غَيْرَ أَنِّي لَمْ أَسْمَعْهُ يَقُولُ إِلَّا خَيْرًا . فَلَمَّا مَضَتْ الثَّلَاثُ لَيَالٍ وَكِدْتُ أَنْ أَحْتَقِرَ عَمَلَهُ قُلْتُ : يَا عَبْدَ اللَّهِ إِنِّي لَمْ يَكُنْ بَيْنِي وَبَيْنَ أَبِي غَضَبٌ وَلَا هَجْرٌ ثَمَّ ، وَلَكِنْ سَمِعْتُ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يَقُولُ لَكَ ثَلَاثَ مِرَارٍ : ( يَطْلُعُ عَلَيْكُمْ الْآنَ رَجُلٌ مِنْ أَهْلِ الْجَنَّةِ ) فَطَلَعْتَ أَنْتَ الثَّلَاثَ مِرَارٍ ، فَأَرَدْتُ أَنْ آوِيَ إِلَيْكَ لِأَنْظُرَ مَا عَمَلُكَ فَأَقْتَدِيَ بِهِ ، فَلَمْ أَرَكَ تَعْمَلُ كَثِيرَ عَمَلٍ ، فَمَا الَّذِي بَلَغَ بِكَ مَا قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ ؟ فَقَالَ مَا هُوَ إِلَّا مَا رَأَيْتَ ، قَالَ : فَلَمَّا وَلَّيْتُ دَعَانِي فَقَالَ : مَا هُوَ إِلَّا مَا رَأَيْتَ ؛ غَيْرَ أَنِّي لَا أَجِدُ فِي نَفْسِي لِأَحَدٍ مِنْ الْمُسْلِمِينَ غِشًّا وَلَا أَحْسُدُ أَحَدًا عَلَى خَيْرٍ أَعْطَاهُ اللَّهُ إِيَّاهُ . فَقَالَ عَبْدُ اللَّهِ : هَذِهِ الَّتِي بَلَغَتْ بِكَ ، وَهِيَ الَّتِي لَا نُطِيقُ .
We were informed by Abdu-aRazaq from Ma'amar from az-Zuhri who said I was informed by Anas ibn Malik who reported: We were sitting with the Messenger of Allah, peace and blessings be upon him, and he said, “Coming upon you now is a man from the people of Paradise.” A man from the Ansar came whose beard was disheveled by the water of ablution and he was carrying both of his shoes with his left hand. The next day the Prophet repeated the same words, and the man came in the same condition. The third day the Prophet repeated the same again, and the man came in the same condition. When the Prophet stood up to leave, Abdullah ibn Amr followed the man and he said, “I am in a dispute with my father and I have sworn not to enter my home for three days. May I stay with you?” The man said yes.
Abdullah stayed three nights with the man but he never saw him praying at night. Whenever he went to bed, he would remember Allah and rest until he woke up for morning prayer. Abdullah said that he never heard anything but good words from his mouth. When three nights had passed and he did not see anything special about his actions, Abdullah asked him, “O servant of Allah, I have not been in dispute with my father nor have I cut relations with him. I heard the Prophet say three times that a man from the people of Paradise was coming to us and then you came. I thought I should stay with you to see what you are doing that I should follow, but I did not see you do anything special. Why did the Prophet speak highly of you?”
The man said, “I am as you have seen.” When Abdullah was about to leave, the man said, “I am as you have seen, except that I do not find dishonesty in my soul towards the Muslims and I do not envy anyone because of the good that Allah has given them.”
Abdullah said, “This is what you have achieved and it is something we have not accomplished.”
(Source of the translation is this article/blogpost with my addition of the narrator chain in italic)
Before going further the narrator chain of this hadith reaches high standards, if there was not a doubt that az-Zuhri might heard from Anas, which was exclaimed by some scholars. A meeting between both can't be excluded, as Anas lived a long time and az-Zuhri is a well known Tabi'i.
Also be aware that nowhere in this hadith there's a mentioning that this Sahabi (who was not a Bedouin as you said) didn't pray in the mosque nor can we conclude that he did. The hadith only says that he performed his prayers on time.
The hadith was compiled as stated above (at least they agreed upon the root Ma'amar from az-Zuhri):
- by 'Abdu-aRazaq عبد الرزاق in his al-Mosannaf المصنف (20559),
- by 'Abdullah ibn al-Mubarak ابن المبارك in his az-Zuhd الزهد (694 or 680) -see here in Arabic- and in his Musnad (1) -see here in Arabic-,
- by an-Nasa-i النسائي in his as-Sunan al-Kubra الكبرى (10699) -see here in Arabic-,
- by 'Abd ibn Humaid عبد بن حميد in his Musnad مسنده (1157) -see here in Arabic-,
- by a-Diya' al-Maqdisi الضياء in his al-Mukhtarah المختارة (2619) -see here in Arabic-,
- by al-Bayhaqi البيهقي in his Sho'ab al-Iman الشعب (6605) -see here in Arabic-,
- by ibn as-Sunni ابن السني in his 'Amla al-Yawm wa al-Laylah عمل اليوم والليلة (754) -see here in Arabic-,
- by ibn 'Abd al-Barr ابن عبد البر in his at-Tamheed التمهيد (Volume 6/p 122) -see here in Arabic-,
- by as-Sam'aany السمعاني in his Adab al-Imala' أدب الإملاء (ص 122 page) -see here in Arabic-,
- by at-Tabarni الطبراني in his Makrim al-Akhlaaq مكارم الأخلاق (72) -see here in Arabic-.
- … (see also a list of takhreej from islamweb here in Arabic)
The qualification and authenticity
Al-Haythami, al-Mundhiri and al-Busiry agreed that the narrator chain is similar to that (if not on the conditions) of both sahihs and al-Albani considered it in first place sahih in his as-Silislah ad-Da'ifah (1/25).
While others as said before doubted that az-Zuhri heard this hadith from Anas due to an existing narration with a different chain: Sho'aib ibn bai Hamzah from 'Oqayl from az-Zuhri who said i was informed by that I don't doubt his speech from Anas. So they claim that az-Zuhri left out the person who transmitted the hadith to him. Among those are a-Daraqotni, al-Bayhaqi, Hamzah al-Kinani and also ibn Hajar who pointed at two weaknesses: a slight uncertainty with Abdu ar-Razaq who said: I was informed by Ma'amar from az-Zuhri from Anas at times and in others I was informed by Ma'mar from az-Zuhri who said: I was informed by Anas. And the fact that Ma'amar who even if he was the most reliable source for the hadith of az-Zuhri he used to make some mistakes and it was also related that his hadith was doubtful during his stay in al-Basra as he was relying on his books which he missed at the time as stated by Ya'qub ibn Shaybah and the weaknes of his hadith in Basra was confirmed by authorities like abu Hatim , imam Ahmad, a-Dhahabi, ibn Rajab and ibn Hajar summarized this saying:
ثقة ثبت فاضل ، إلا أن في روايته عن ثابت والأعمش وهشام بن عروة شيئا ، وكذا فيما حدث به بالبصرة .
Trustworthy of high standards an manners, but there's something (weakness) in his narrations form Thabit, al-'a'mash and Hisahm ibn 'Urwah and also in what he narrated in al-Basra. (Source islamqa #147249 -in Arabic-)
In the same fatwa we can read the final qualification of al-Albani after reading al-Bayhaqi's qualification from his "Da'if at-Targheeb wa at-Taarheeb" (the book of imam al-Mundhiri to who he refers):
In the following I'm translating from Arabic language, as these translations are of my own takethem with the necessary care
هو كما قال ، لولا أنه منقطع بين الزهري وأنس ، بينهما رجل لم يسم ، كما قال الحافظ حمزة الكناني ... ثم الناجي ، وقال [ أي : الناجي ] : وهذه العلة لم يتنبه لها المؤلف [يعني : الحافظ المنذري] .." . ثم قال الشيخ الألباني رحمه الله ، بعد ما نقل إسناده عن عبد الرزاق :
It is as he (the author al-Mundhiri) said if there was not the cut between az-Zuhri and Anas, between both there's a not named man, as stated by al-Hafidh Hamzah al-Kinani: … and the an-Naji who said (refers to an-Naji): and the author(refers to al-Hafidh al-Mundhiri) missed this issue (weakness) …" After that sheikh al-Albani may Allah have mercy on him said after quoting the isnad from Abdu ar-Razaq:
" وهذا إسناد ظاهره الصحة ، وعليه جرى المؤلف والعراقي في "تخريج الإحياء" (3/187) ، وجرينا على ذلك برهة من الزمن حتى تبينت العلة ؛ فقال البيهقي عقبه (5/265) : "ورواه ابن المبارك عن معمر، فقال : عن معمر، عن الزهري، عن أنس . ورواه شعيب بن أبي حمزة عن الزهري ، قال : حدثني من لا أتهم عن أنس ... ، وكذلك رواه عقيل بن خالد عن الزهري" . وانظر: أعلام النبلاء(1/109) ، ولذلك قال الحافظ عقبه في "النكت الظراف على الأطراف": فقد ظهر أنه معلول" . انتهى .
And this is an isnad which apparently is sane, and this appearance is what the author and al-'Iraqi in his "Takhrij al-Ihya' (3/187)" relied upon and we follwoed this for a while until the issue got clear: As al-Bayhaqi said afterwards (5/265): "And it was narretd by ibn al-Mubarak from Ma'amar, who said: From Ma#amar from az-Zuhri from Anas. and it was narrated from Sho'ayb ibn abi Hamzah from az-Zuhri, who said: I was informed by the person I don't doubt from Anas .. and it was also narrated by 'Oqayl ibn Khalid freom az-Zuhri (this way) See also in Siyar 'Alaam an-Nubala' (1/109). That's why al-Hafidh commented it after citing it saying: "An-Nakt (refers to a small spot which is unlike his surroundings) is the information which one finds in small parts"
"ضعيف الترغيب" (2/247) هامش (1) .
Footnote (1) in da'if at-Targeeb wa at-Tarheeb (2/247)
There's a similar narration in al-Bayhaqi's Sho'ab (see here -in Arabic), but this narration also includes unknown narrators and therefore it has a high level of weakness.
So basically the hadith is discussed among scholars. And the issue is whether or not az-Zuhri heard it from the sahabi Anas. If he didn't hear it directly the issue is the unknown reporter between both. Else the narrator chain has a high level of sanity and trust that is similar to that of the two sahihs.
This article basically discusses four different narrations (the main difference is in the narrator chain at least 3 of them are students of az-Zuhri reporting from their teacher the only one who said az-Zuhri heard from Anas was Ma'amar) including the above discussion and an explanation of possible issues in the content.