Well I'm not the best person to get advice from, since I'm perpetually complaining about not having enough female friends, but I'll give you what I know.
* Be open with your feelings. "I had a great time", "I love talking on the phone with you" etc., are things that two guys might not say to each other, but girls would.
* Be vulnerable. Be willing to show parts of yourself you're not proud of. This isn't strictly required, but it helps break the ice. Often when it feels like there is distance, it's because people are holding back.
* Smile a lot.
* I have not noticed women talking with each other about bodily issues, periods, birth control, etc., so I don't think you'll have problems with that. If they do, you can always say you "don't get periods anymore for medical reasons". No one will pry.
But here is what I've found: Eventually I WILL have to tell them who I am. When we trust each other, and they want to know details about my life, it's hard to hide who I used to be. Of course I'm divorcing my wife, have two kids, etc., so maybe it's harder for me.
Hope this helps. Let us know how it goes.