I am bisexual as well, but I have not come out yet. I am proud of you for realizing this about yourself and coming out to people you trust. My family is very conservative as well, so I understand that fear all, ALL too well.
There is absolutely nothing wrong with wanting to be with a woman, and feeling that fear of being around men. I understand that too, from past experience. Just take it a step at a time.
I would come out to your therapist, and if it doesn't go well, you can always find another one. There are many that are friendly toward us.
Don't give up and don't loose hope. We are here for you.
- Sarah