I guess I can kind of see what you mean. The thing is, bisexuality doesn’t really have a clear line, you can be more attracted to one gender than the other and still be bi. I read somewhere (I’m not sure if this is accurate) that for example you can have really strong sexual feelings towards one gender, and have really strong romantic feelings towards the other that don’t include sexual desires whatsoever.
But if you want to have a relationship with a woman, I feel like you are bi. I don’t see why you would be gay and still have the desire to be in a relationship with a woman and have even a little desire to have sex with them. In the case that you are, I don’t think you have to tell your parents anything since you’re still attracted to girls right? Though I guess things would get difficult if you started dating/wanted to marry a guy.