This isn't a bike problem, it's a mental issue. Yes, there are crank forward bikes (google), which allow what your GF wants. They are OK for short trips on the flat, but not too much more IMO. She just has to suck it up and learn how to mount, start, and stop a properly setup bicycle. There's not really another answer. Little used parking lots can be good for this sort of thing. It's a matter of doing it over and over until it feels OK to her and she's stopped making mistakes. You know how to stop a bike without falling over. Teach her how. It's just fear, that's all. Fear can be overcome.
My wife is 5'1", rides an MTB converted to drop bars. She runs 1" tires which are possible to find. It's a good solution.
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