Where was the Prophet allowed to go out in this hadith?

Question

قَالَ أَبُو بَكْرٍ مَا جَاءَ بِهِ فِي هَذِهِ السَّاعَةِ إِلاَّ أَمْرٌ‏.‏ قَالَ ‏ "‏ إِنِّي قَدْ أُذِنَ لِي بِالْخُرُوجِ ‏

... Abu Bakr said, 'There must be something very urgent that has brought him at this hour.' The Prophet (ﷺ) said, 'I have been allowed to go out'

See full hadith in Sahih Bukhari

I can come and think of two different interpretations:

• Habasha, where some sahaba migrated
• Medina, the hijra

I am not sure if I am missing some more possible interpretations but I also come and think about a third interpretation (which might be less valid):

• The event when some muslims, marched out in rows to Kaaba

Where was the Prophet allowed to go out in this hadith?

When answering, please provide references such as different commentaries of the hadith, as for instance Fath Al bari by Ibn Hajr Asqalani or others.

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Comments about the third interpretation:
I don't have much references about the third interpretation (about them marching out to Kaaba), except this and this video. In the hadith, it seems like Umar told the Prophet to march directly after his conversation to Islam, while I have heard that Umar first went out to some of the mushrikin in Quraysh, telling them about him becoming a muslim (see the above video), therefore the marching out might not have happened directly when he suggested that to the Prophet. This might then give time to the Prophet to later visit Abu Bakr as in the hadith saying: 'I have been allowed to go out (i.e to march)'.

Answer 1

Its about the migration to Medinah. See the complete variant here

فَقَالَ ‏"‏ أَشَعَرْتَ أَنَّهُ قَدْ أُذِنَ لِي فِي الْخُرُوجِ ‏"‏‏.‏ فَقَالَ يَا رَسُولَ اللَّهِ الصُّحْبَةُ‏.‏ فَقَالَ النَّبِيُّ صلى الله عليه وسلم ‏"‏ الصُّحْبَةُ ‏"‏‏.‏ قَالَ يَا رَسُولَ اللَّهِ عِنْدِي نَاقَتَانِ قَدْ كُنْتُ أَعْدَدْتُهُمَا لِلْخُرُوجِ‏.‏ فَأَعْطَى النَّبِيَّ صلى الله عليه وسلم إِحْدَاهُمَا وَهْىَ الْجَدْعَاءُ، فَرَكِبَا فَانْطَلَقَا حَتَّى أَتَيَا الْغَارَ، وَهْوَ بِثَوْرٍ، فَتَوَارَيَا فِيهِ، فَكَانَ عَامِرُ بْنُ فُهَيْرَةَ غُلاَمًا لِعَبْدِ اللَّهِ بْنِ الطُّفَيْلِ بْنِ سَخْبَرَةَ أَخُو عَائِشَةَ لأُمِّهَا، وَكَانَتْ لأَبِي بَكْرٍ مِنْحَةٌ، فَكَانَ يَرُوحُ بِهَا وَيَغْدُو عَلَيْهِمْ، وَيُصْبِحُ فَيَدَّلِجُ إِلَيْهِمَا ثُمَّ يَسْرَحُ، فَلاَ يَفْطُنُ بِهِ أَحَدٌ مِنَ الرِّعَاءِ، فَلَمَّا خَرَجَ خَرَجَ مَعَهُمَا يُعْقِبَانِهِ حَتَّى قَدِمَا الْمَدِينَةَ

... The Prophet (ﷺ) said, "Have you noticed that I have been allowed to go out?" Abu Bakr said, "O Allah's Apostle, I would like to accompany you." The Prophet (ﷺ) said, "You will accompany me." Abu Bakr said, "O Allah's Messenger (ﷺ)! I have got two she-camels which I had prepared and kept ready for (our) going out." So he gave one of the two (she-camels) to the Prophet (ﷺ) and it was Al-Jad'a . They both rode and proceeded till they reached the Cave at the mountain of Thaur where they hid themselves. Amir bin Fuhaira was the slave of Abdullah bin at-Tufail bin Sakhbara `Aisha's brother from her mother's side. Abu Bakr had a milch she-camel. Amir used to go with it (i.e. the milch she-camel) in the afternoon and come back to them before noon by setting out towards them in the early morning when it was still dark and then he would take it to the pasture so that none of the shepherds would be aware of his job. When the Prophet (and Abu Bakr) went away (from the Cave), he (i.e. 'Amir) too went along with them and they both used to make him ride at the back of their camels in turns till they reached Medina ...

Also see this variant:

، فَلَمَّا أُذِنَ لَهُ فِي الْخُرُوجِ إِلَى الْمَدِينَةِ لَمْ يَرُعْنَا إِلاَّ وَقَدْ أَتَانَا ظُهْرًا، فَخُبِّرَ بِهِ أَبُو بَكْرٍ فَقَالَ مَا جَاءَنَا النَّبِيُّ صلى الله عليه وسلم فِي هَذِهِ السَّاعَةِ، إِلاَّ لأَمْرٍ حَدَثَ، فَلَمَّا دَخَلَ عَلَيْهِ قَالَ لأَبِي بَكْرٍ ‏"‏ أَخْرِجْ مَنْ عِنْدَكَ ‏"‏‏.‏ قَالَ يَا رَسُولَ اللَّهِ إِنَّمَا هُمَا ابْنَتَاىَ‏.‏ يَعْنِي عَائِشَةَ وَأَسْمَاءَ‏.‏ قَالَ ‏"‏ أَشَعَرْتَ أَنَّهُ قَدْ أُذِنَ لِي فِي الْخُرُوجِ ‏"‏‏.‏ قَالَ الصُّحْبَةَ يَا رَسُولَ اللَّهِ‏.‏ قَالَ ‏"‏ الصُّحْبَةَ ‏"‏‏.‏ قَالَ يَا رَسُولَ اللَّهِ إِنَّ عِنْدِي نَاقَتَيْنِ أَعْدَدْتُهُمَا لِلْخُرُوجِ، فَخُذْ إِحْدَاهُمَا‏.‏ قَالَ ‏"‏ قَدْ أَخَذْتُهَا بِالثَّمَنِ ‏"‏‏.

Rarely did the Prophet (ﷺ) fail to visit Abu Bakr's house everyday, either in the morning or in the evening. When the permission for migration to Medina was granted, all of a sudden the Prophet (ﷺ) came to us at noon and Abu Bakr was informed, who said, "Certainly the Prophet (ﷺ) has come for some urgent matter." The Prophet (ﷺ) said to Abu Bark, when the latter entered "Let nobody stay in your home." Abu Bakr said, "O Allah's Messenger (ﷺ)! There are only my two daughters (namely `Aisha and Asma') present." The Prophet (ﷺ) said, "I feel (am informed) that I have been granted the permission for migration." Abu Bakr said, "I will accompany you, O Allah's Messenger (ﷺ)!" The Prophet (ﷺ) said, "You will accompany me." Abu Bakr then said "O Allah's Messenger (ﷺ)! I have two she-camels I have prepared specially for migration, so I offer you one of them. The Prophet (ﷺ) said, "I have accepted it on the condition that I will pay its price."