It does sound like your mom has some misunderstandings about bisexuality, but it also sounds like it isn't something she's hostile to, which is a good sign.
It may be that if you come out to her she'll try to argue with you, or say you're too young or inexperienced to know your sexual orientation, and if that happens I think your best bet is to let her know that you
are the person who is most likely to understand your own feelings and attraction, and to ask her to respect what you've told her about your identity even if she does feel like you can't be certain.
It could even be that you talk to your dad first, and let him know you'd like his support if your mom says or does certain things. Some people like to talk to their parents together, if possible, and others might want to have one-on-one conversations; either way is fine.
If you think it would be helpful (you can read it beforehand to see how you like the information provided there), you could give your mom something like this pdf from PFLAG that has a basic guide for parents when their children come out to them: https://pflag.org/resource/our-children