Being bi and personal friendships

As of late I've noticed something about myself. I'm having a awkward time being around women now that I'm fully aware of my biness. I find myself thinking things like "Could I sleep with her?" Or sizing women up. I know that with women things get very personal. I mean, when one woman finds another woman who she feels that she can just be open to, a lot of personal information gets exchanged forming a rather intimate emotional bond. This makes it easy to get attached. My problem is I'm having a difficult time learning how to be personal and just a friend without thinking about sleeping with them. I don't think this way with every woman I meet just the ones I start to develop a friendship with. I guess in my mind I feel that if things can get so deep and personal then the next step is physical intimacy. I want to be able to have a close, emotionally intimate friendship with another woman without feeling as though because I'm bi I have this obligation to feel open to the idea of having sex with her. I've done some soul searching and realized that I have some hidden assumptions towards myself in regards to my feelings about sex and being bi and they are:

1) that I should always be available sexually
2) that every relationship must become sexual, eventually
3) that I should always be on the prowl and checking out everyone

I tell myself that being bi isn't all about having sex yet whenever I meet a nice woman and start to get to know her I start to think of her in sexual ways. I feel bad about this because I feel like I'm objectifying women or sexualizing every friendship. I feel incredibly uneasy when a woman starts to get close to me and share her personal life with me because I don't know how to be personal without the desire to feel sexual towards her and heaven forbid if she's attractive. When I do things or say things I'm not sure if I'm being a caring friend or being seductively charming. I'm used to being this way with men so I never know if I'm really being sincere and caring or if I'm just trying to charm my way into their heart.
I have to say that love, sex, friendship, emotional intimacy, flattery and charm are all a blur in my mind. I really want to develop close friendships with women without feeling as though because we're so close that I have to consumate the friendship with sex.