She might suffer from vaginismus, a condition that makes the vagina tense up during sex and makes it very painful. It has nothing to do with your penis size or being gentle or lube. There are exercises she can do to overcome this condition, just take her to a doctor instead of causing her more pain
Probably she should see a gynecologist and she may need surgery to open the hymen
In her shoes, I would see a gynecologist. Some women do have a much thicker hymen than average, that might be what she has.
Well, it seems like you've tried the first line of advice, which is using lots of lube and going slowly. If you can't fit two fingers without her bleeding, though, you won't be able to fit a penis right now, and you shouldn't try if it's making her bleed. Definitely don't try to force it. She should maybe see a gynecologist to make sure there's nothing medically wrong, since it causes so much pain. In the mean time, the best thing is probably to work up to it with variable sized toys. An anal training set might actually be a good place to start, because they have various sizes of tapered toys that start at a very small size. You can work on them together while she's really aroused, since that makes penetration easier. She should also try to masturbate with them, using plenty of lube, so that she can gently and gradually stretch herself out. They also make inflatable toys, which can be inserted and then inflated just enough to stretch a bit. When she's worked up to it, and you're ready to try intercourse again, let her be on top and control the pace.
Good luck, and have fun!