If you love him more than her then it makes sense to date him, I wouldn't be worried about what others think of you because you know you won't be alone to deal with it even if you were both out to everyone, which you don't need to be. There is nothing wrong with keeping your relationship hidden, after all no one needs to know so what does it matter? Of course, that all depends on whether he wants to keep it secret or not, and he is not out as gay or bi as it is so I am doubtful, besides, you have to agree to be out if he wanted to be. I think, you know you like the girl, and you aren't so sure about him, so I think this is a perfect opportunity to experiment with sexuality to discover yourself better. At least if you date him, it provides a foundation for which to build future relationships on, you will gain some experience.
Really, go out with the one you feel most comfortable, and love the most, I personally wouldn't recommend dating both at the same time, that has too many potential consequences.
You shouldn't worry about bullying, straight people/couples are bullied as well, and there is no need to show off a relationship to others, because it is personal and none of their business.
