You don't have to come out or anything, just don't go if you don't want to deal with the awkward feelings. Even my best friends wouldn't be weirded out if I said "I don't think I can make it to *insert event here*, but thanks for inviting me!"
People have lives, you know? Work and school, or illnesses that get in the way are just a few things that could prevent you from going to your friend's hen party. Just be apologetic and chill about it all, and the response will typically be a positive one.
And if you're worried about being asked to be a bridesmaid, it's okay to say no. I know plenty of girls who have said no. It's not their thing, you know? If someone gets offended over something so trivial, they're probably not worth talking to in the first place. Good luck, mate.