I'm starting to hate myself

I just got a phone call from a girl I had worked with a few times this past week. She is an audiologist at the ENT clinic I was at. We worked together a few times and seemed to hit it off a bit. I do find her attractive and had a good time talking to her while we were working on patients. At the end of the rotation she said she had a great time with me and that we should get together sometime. She had previously mentioned that I should come and hang out with her and her friends at uptown sometime, which I heard but let slide because I knew the implication behind her proposal. I thought I had gotten off the hook until the last day. I couldn't just walk away and hurt her feelings so of course we exchanged phone numbers. I had forgotten the issue until she called just now. She left a message asking if I wanted to get together for coffee or drinks sometime this week.

I have a problem. This is not a new or even rare occurrence. I should have figured out the perfect way to go about this by now. I just feel as though I have to spare everyone's feelings. I have no idea which is better. Should I stand firm with an initial denial or brush her off later in the week if she calls. I have no idea which is worse. I honestly like this girl and don't want her to feel that I am not going out with her because she is lacking in qualities or characteristics that men find attractive. At the same time I'm not out which means I need to protect my secret. I can't just tell her the real reason why there will never be a relationship.

Life would seemingly be so much easier if I was out. I really need to deal with this soon.