Can reproduce it as well, without any mods except Traffic++.

I had a similar thing happen to me. The Traffic++ roads work by only allowing cars that belong to a certain category drive on them. You can use the lane changer to double check that it's working. Cars that are parking can disregard road rules if it takes too long to do a detour or drive to a different parking space; hence they will drive the wrong way on one way streets, use sidewalks, clip through buildings, disappear and use bus lanes. You can click on vehicles to find out what they are doing (parking, driving home, driving to work, etc...). I don't know why cars engage their "find a parking spot" code so early, or why the trucks are in the bus lanes.

Some ways you can fix this (that I used in my cities) are you could make your bus lanes separate from normal intersections/roads or make them slightly longer or slower than normal streets to prevent normal cars from using them. Hope this helped!

PS.
don't make your bus stops so close together. That defeats the whole point of busses