There is a hadith where the Prophet asked Asma if she wanted a ride in his camel but she refused because her husband doesn't like her being with other men.
This is the hadith which is narrated by Asma herself:
"When az-Zubayr married me, he had neither land, nor wealth, nor slave, nor anything else like it, except a camel to get water and his horse. I used to graze his horse, provide fodder for it, look after it and ground dates for his camel. Besides this, I grazed the camel, made arrangements for providing it with water and patching up his leather bucket and kneading the flour. I was not very good at baking the bread, so my female neighbors used to bake bread for me and they were sincere women. And I used to carry on my head, the date-stones from the land of az-Zubayr which the Prophet sallallahu 'alayhi wa sallam had endowed him and it was a distance of two miles from Madinah. One day, as I was carrying the date-stones upon my head, I happened to meet Allah's Messenger sallallahu 'alayhi wa sallam, along with a group of his Companions. He called me and told the camel to sit down so that he could make me ride behind him. I felt shy to go with men and I remembered az-Zubayr and his ghirah (ghirah is the sense of pride that a man has which causes him to dislike his wives, daughters or sisters from being seen or heard by strangers - it is this ghirah which makes a man protective about his women) and he was a man having the most ghirah. The Messenger sallallahu 'alayhi wa sallam understood my shyness and left. I came to az-Zubayr and said, 'The Messenger of Allah met me as I was carrying date-stones upon my head and there was with him a group of his Companions. He told the camel to kneel so that I could mount it but I felt shy from him and I remembered your ghirah.' Upon this az-Zubayr said, 'By Allah, the thought of you carrying date-stones upon your head is more severe a burden to me than you riding with him.' I led this life of hardship until Abu Bakr sent me a female servant who took upon herself the responsibility of looking after the horse and I felt as if she had emancipated me."
[Reported in Sahih al-Bukhari (eng. trans.) vol. 7, p. 111, no. 151]
The reason I asked if it would have been a sin is that sister in laws are not mahrams as stated before on this site in this question:Is the brother in law (sister's husband) a mahram in Islam? and Asma was a half-sister-in-law of the Prophet as Wikipedia states:
Her half-sisters were Aisha and Umm Kulthum bint Abi Bakr, and her half-brothers were Abdul-Rahman ibn Abi Bakr and Muhammad ibn Abi Bakr.
Also the Prophet forbade being alone with a non-mahram. He said:
“No man should be alone with a woman unless there is a mahram with them.”
Narrated by al-Bukhaari (1862) and Muslim (1341).
And he (blessings and peace of Allah be upon him) said:
“No man is alone with a woman but the Shaytaan is the third one present.”
Narrated by al-Tirmidhi (1171) and classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
The above states that it is haram to be alone with a non-mahram.
Question: If Asma bint Abu Bakr accepted the Prophet's offering of a ride, would the Prophet have committed a sin?
My guess is that in the hadith, it mentions that the Prophet was with Companions and one the Companions might have been a mahram so it wouldn't have been a sin but I'm not sure.