They definitely change.

I've been experimenting and stalking Civs all day. They will change from one line to another even if they have to walk and\or cross a road to the next stop.

Putting them all on a shared stop makes it easy for them to change, but can create bus congestion as only one bus can interact with the stop at a time. This bus-jam will then create a traffic jam as well.

Having a row of different line bus stops lets them each interact with their own stops, while still being fairly close for passengers changing. If you've ever been to a major shopping center or train station you've probably seen what I'm talking about here.

Even if Civs have to cross a road, they'll do so to swap to a new line colour if that's the best route for them. If you have an intersection nearby they'll use it, although that will mean waiting for an opportunity so you might want to consider a pedestrian bridge across the road. This works best at interchange areas with lots of loops converging before spreading out.

Direction matters, if your stops can't keep up with the demand you might want to add a reverse lane. The same bus route, but backwards. I like to pair the colour as a light\dark of the same to make it easier to see them. This way civs will favor one side of the road over the other so both mirrored lines get an even split of passengers rather than one overloading and constantly trying to catch up.

Another option is an express route of the same root. Note where lots of Civs get on\off on the route and redo a second overlapping line that only stops at those stops.

I've also personally stalk civs who took 2 or 3 different lines to get to where they want, even if they had to walk a little between stops. it's possible they'd take even more buses as 3 was the maximum they would need in the city I had planned out for the experiment.

Oh, and one last thing. It worked best to have lines that weren't too big or they'd run into the same problem have having too many civs for the buses to hold. segmenting the buses so I had some residential loops converging on a commercial area loop, that connected to an industrial loop on the far side worked pretty well.