QUIET Exercise Bike Under $300?
Assuming you already have a bike, have you looked into a trainer? Since you're not buying as much equipment, essentially just the resistance unit, you can get much better quality without spending as much.  I got a CycleOps Fluid2 and it's pretty quiet, and also folds down pretty small which would probably be beneficial in an apartment.  There's quite a wide range of them, and I understand that most of them are pretty quiet as long as you stay away from the cheaper "wind" trainers.