Many people still believe negative stereotypes about bisexual people, including that bisexuality is just a phase. While some people who initially identify as bisexual do eventually realize that they are actually gay or straight, the majority of bisexual people continue to identify as bisexual throughout their lives. Remember, over half of the LGBT+ community is bisexual. It may help to show your mom material written by older bisexuals, such as bi activist Robyn Ochs, to show her that bisexuality is not a phase one grows out of.
If you meet someone you like and want to date, try not to let other people's misconceptions prevent you from being with the person you want to be with. Your relationships are for you and for the person you are in a relationship with, not for anyone else. Don't worry about what other people will think. Your happiness is more important than their bigotry.
You can be bisexual and be more attracted to women than to men. You don't have to be equally attracted to men and women to consider yourself bisexual. Perhaps you are a lesbian, or perhaps you are bisexual with a preference for women. Only you can determine this. To figure this out, ask yourself if you still find yourself attracted to men at all, or if you are only interested in women.