You mean a full size bike? I'd say you are badass for even trying! Sorry, no help there. But I'm 5 ft, 2 inch...
Maybe a foldable bike is an idea? I absolute love my second hand brompton, it allows me to optimize the use of public transport without the "hassle" of towing a bike along in the train and having to stand all the way etc. You are allowed to take them anywhere, they are even said to fit in the handluggage space of an airplane (no personal experience, though). And if the trains crowded, I always have a seat: the sadle of my folded bike.