2 issues here: First is your unhappiness with this camp. Second is your sexuality and the decision to tell your mom. Let's seperate them, they are very different and require 2 different plans!
First, if you hate camp, you might tell your mom you hate camp, give her the GENERAL reasons, like 'they're all small minded', or 'they bully me', which is, afterall, the truth, but not so revealing as to overshadow your current, immediate concern of getting out of camp.
The decision to tell your mom about your sexuality is a much more complex one, and you should give it alot of thought first. The decision to share anything personal (not just about sexuality) should be about helping the relationship between you and the other person, not about 'getting something' , like out of camp, or feeling less guilty, etc. This requires a bit more planning and soul searching, but for the current issue, I think you can probably get out of camp without doing something that might be premature and cause more problems for you than the stuff at camp.