Bicycle wheels may not be the best choice. They're intended to take a
force orthogonal to the axle. You're asking it to take a parallel
force. One bearing is going to take the load and the other nothing.
The force is also at the edges of the race. Not ideal, to say the
least.


It would need to be a big load over a big period of time
to affect a bicycle axle & bearings ...
I doubt this school project will wear out the bearing race ..
I suspect that the teacher is looking for something cheap
free and readily available ; and functional.
ie: old bicycle wheels
John T.