I haven't told my girlfriend yet, and I am worried about how she will react. I love her and I don't want to end the relationship, but I also know that she would probably be upset if she found out. Is it possible to tell her without causing too much drama?
First, remember that your girlfriend isn't a homophobe. Her reaction may be surprising, but it will likely be based on her own experiences and opinions. She may be pleasantly surprised by the news, or she may have preconceived notions about bisexuals that will need to be addressed. She may need reassurances that you will still love her, and that you won't sleep with men or treat women differently.
It's important to prepare yourself for your partner's response, so you can answer her questions and concerns in a way that is respectful and honest. This can be a difficult conversation, so it's best to choose somewhere private and calm, like your home or a coffee shop. Be ready to listen and support her as she goes through her reactions, whatever they are.
You should try to get a sense of her feelings about gay people before you bring up the subject, so you can be more prepared for how she will respond. For instance, you could mention a film or TV show that depicts homosexuality in a positive light and ask her what she thinks about it. You could also ask if she has any gay or bi friends, and you could discuss those relationships.