Buying used now is a sensible alternative. It will also give you some more experience on a bike so that you can make a much more intelligent decision when you get the money for a better bike.
It is an unfortuate situation that when we are young, we have zero tolerance for patience or waiting to get the thing we desire most. That is standard and normal, and when we can't get it we blame those around us instead of recognizing that if we want it enough, it is up to us to make it happen.
Don't be too hard on yur Mom for being "unreasonable". she's just being frightened for your safety. And, believe it or not, she's saying she loves you.
Get as much bike as you can, with the money you have.
Also. I would try to come up with a better storage system than the bedroom.
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ljbike