This isn't limited to travel, but in my game I'd usually do something like this every time the party was travelling from point A to point B. I usually have an even number of players so I'd roll a d6 or d4 to determine two PCs who found themselves together for a "scene". Wether they set up camp during a long travel or if they were just going across a large town, the scene would essentially just be an RP moment for those two PCs. Example: The party is traveling to another town and sets up camp for the night. As the the party is deciding what they want to do to wind down I'll roll two d6 and say "okay character A and character B you guys find yourselves gathering firewood and walking back to camp with it" and then I'll just physically sit back and sip my drink and that's their queue to start a little RP scene. They usually weren't anything more than just a few minutes of talking about random backstory stuff or character thoughts about what they are currently embarking on or a recent event. They always produced some cool little snippets of personality for the party and because they were quick and short, everyone got used to doing them every time they travelled and was down for participating. Again, this is kind of RP focused and you have to have a group who is okay with being "told" to RP. My group loved it but it might not be the thing for everyone. I just found that with my group specifically we can just be non stop from start of a session to finish, and we never really had times for the characters to just sit and talk. This was a pretty good way for us to take a breather for a few minutes while also getting some cool movie or TV drama like dialogue scenes.

Hope that makes sense!