How many flights of stairs does OP need to climb up to her apartment? And how wide is the staircase? I'm female myself and I wouldn't want to carry around a full bike up the stairs every day. Our staircase is not so wide either so the logistics of making sure I don't bash my bike around would cause stress for me even if the bike was not so heavy. I also don't think $500 would get you a light enough bike, unless it was a road bike which OP does not want.

I suggest going the folding bike route. Even if folding bikes are heavier than some full-on road bikes, their compactness make them MUCH easier to carry around. Many models can be fitted with a pannier as well.