You can get a decent work-out on a crappy rental bike, it's just not as fun. Think of it as a kind of cross training
Your Mom should understand your bike habit by now. It is not like you are bringing home a German Shepard, jeesh! Could you find a fellow cyclist in your Moms building maybe?
If you really get stuck it is possible that you could store your bike at my place in Brooklyn, if you have no other possibilities. I live in a big loft. We can hang it in a locked hallway with my other bikes. I will give you keys to the building and the hallway so you can arrive/go as you please. Your Mom has to put me in the will, though..