If you go slowly, you will develop the relationship to a point of trust. Before you get close and attach, if the friendship doesn't work out and falls by the wayside, it won't be so painful. It will be in the early stages before attachment. So it's easier (less painful) to let the relationship slide during this period. It's like a gettting to know you period when each person is deciding if they will put effort into the relationship. So Zen, my main suggestion is just to go slowly. See if you can build up a casual friendship or two where the rejection stakes aren't so high.

Lemon mentioned friendships at work. I agree this is a less threatening place to build a friendship as you are both there all day anyway--you don't have to risk as much, at least at first. A friendship at work can start just by talking to a co-worker about what you did over the weekend. And you can talk about non-task related things at work too, e.g. "can you believe our insurance premium went up so much this year?" or "I can hardly wait until we move to the new building", etc.

I don't have many friends either, so I probably shouldn't be giving any advice. For me, a lot of it is time. I feel run ragged by work, being a mom, keeping my house from falling apart, etc. There is not a lot of time for friendships, not to mention a romantic relationship. Somehow, I have to learn to manage my time better to have relationships.