I've been trying to find some consistency in the bike behaviour, but they act really weird and unpredictable.
What I've found is that if the sim is inside and you tell them to bike to a place outside, they will get on the bike (while still inside) and ride outside. Except in buildings like all the uni buildings where they have to cross stairs, they will only bike until they reach the stairs and then run the rest of the way. They won't get back on the bike once they're outside.
Only when they live on the uni lot (like in the dorms), they won't use the bike to get to class and they won't phase out (like they do when they live anywhere else), so they're always late for the first class of the day. But when they finish one class and their next class is in different building, they will get on the bike to get to the next class. Basically the only way to make sure your sim is always on time for class is to make them not live on campus.
They generally seem to be unable to use the bike when they autonomously go somewhere, like when they go to work or school, but if you manually tell them to go somewhere they will use the bike instead of walking, unless they have to move a very short distance.
It's actually the same issue with the jetskis, except it's not as bad because they can't use it indoors.