It sounds like your parents understanding and acceptance of your sexuality is very important to you. I can understand you not wanting to feel condemned for feeling __. That's very human.

I just see the answer to your Q, about what can you do to make your mom see that you aren't going through a phase or simple confusion, is to let go of that for now. Your mom may just need time to adjust to the concept as you adjust to living your life the way that you'd like.

Personally, I don't understand why your mom's confusion of your sexual interest being bisexual (rather than lesbian) so distressful to you. Just curious why that particular point..... Just my opinion.