The Oz Nidberu quotes the Mekor Halachah (Vol. 2, on Shabbos 17, Birur Halachah pg. 46, ois 22) who already writes: It’s forbidden to sit next to someone who is an ervah if one will end up touching. Even in places where it is normal to sit together, such as on a bus, as any touching of an ervah, even via clothing is forbidden מפני קירוב בשר דאסור מהתורה – as an enactment so that one doesn’t come to touch actual skin. Or it is forbidden as we are worried one will come to benefit intentionally. He also quotes Tosfos in Sanhedrin (37a) which says that מתחממין זה בזה - getting heated up from each other, is a problem. (The reason the Gemara mentions “sleeping in one bed”, is because then the issur is even without touching, however, when touching even just sitting together is a problem.)
In ois 23 the Mekor Halachah writes: “Therefore, it is permissible to sit next to a woman when traveling on a bus, provided one is careful not to touch even her clothes. In pressing circumstance perhaps, we can even allow the touching of clothes, if the clothes are thick and there is no heat being transferred.”
The Oz Nidberu continues: It’s clear that he (the Mekor Halachah) holds that in pressings circumstances one can be lenient, and the lashon “perhaps” that the Mekor Halachah uses is not specific. If so, regarding the question of sitting next to a kallah, it’s not up to me to decide what is considered a pressing circumstance, and each person needs to determine himself what is considered a pressing circumstance. Even if one is unsure if he is in a pressing circumstance he may be lenient, as strictly speaking it’s permissible.
Distinction Between Summer and Winter
The Oz Nidberu further writes: The main concern is when traveling in a taxi in the winter when it’s very hard not to touch, as people have long heavy coats and thick clothing. However, on the other hand, the clothes are thicker and heat from the women’s body isn’t transferred, and Tosfos writes מתחממין, which refers specifically to body heat.
In the summer people wear less clothing and heat is transferred more easily, however, even in the summer and traveling by taxi it’s possible to be careful, and if the man and lady accidently bump into each other when the taxi takes a sharp turn it’s not a problem. Even if a man and woman are sitting on the back seats of the bus, if they are careful, they can avoid bumping into each other.
The Oz Nidberu concludes: In short, the yesod [foundation] for the heter is that there is no source to forbid. The reason to forbid is based on the Gemara in Shabbos (13a) which says, “It’s forbidden for a man to sleep in the same bed as a woman, even if they are both dressed”. There are a number of reasons to differentiate between the Gemara and our case: Firstly, sitting may be different to lying in a bed, however, it’s logical to say that sitting is included in the issur of the Gemara, if body heat is being transferred, like Tosfos speaks out. However, if they are both wearing winter clothing, when the heat comes from the clothing and not the body it’s ok. If they make an interruption between them with clothes they aren’t wearing, certainly it helps. If the clothes are thick, even when wearing them it should be good, and we don’t say they are nullified to the body like by Shabbos. It makes no difference if the woman is married to someone else, or is just a kallah, she is still considered an ervah.
Sometimes It's Better to Sit Next to An Ervah, Than It Is to Remain Standing
The Beis Yechezkel (Maamer Kedushas HaYodayim Vechush Hamishush ois 32) quotes the Mekor Halachah on Shabbos (Emek Halachah, siman 17) who says based on Tosfos in Sanhedrin (37a), that there is only a heter for a man to sit next to a woman if they don’t heat each other up due to being close together, if they do, then even if there is a garment in-between them it’s a problem.
However, the Oz Nidberu writes that sometimes it’s better to sit next to an ervah on a bus than it is to stand. For example, if one has the option of sitting towards the front of the bus next to a woman, or standing somewhere near the back, it’s better to sit. If one sits, he won’t look at ervah, however, if he stands at the back, he is likely to see all the women inappropriately dressed, and certainly in such a case it’s better to sit. על פי דין ועל פי מוסר - according to both halachah, and mussar. He concludes: ודברי פי חכם חן – the words of a chocham should find grace.
The Oz Nidberu adds: Those who are careful will choose a row with just two seats on, and the woman will sit next to the wall and the man next to isle, sitting tilted towards the isle, and they can sit in a way they will avoid bumping. (See however, Shu”t Shevet HaLevi 4:136 who seems to prefer standing).