I'm going to weigh in as a transgender man (female to male). 

I prefer to think of myself as a good person-- I've never done anything illegal, and I try to be kind and courteous to all I meet. I've definitely never felt the need to bother or harass anyone in any bathroom (men's or women's) because that's kind of a jerk thing to do. I do my business, wash my hands go on about my day. I can safely say that that's all we, the members of the trans and gender non-conforming community, really want-- to be allowed to go to the bathroom in peace. We're more likely to be hurt in the bathroom by the bigoted and intolerant than anyone else is by our presence-- and legislation like this will make it even more likely that a trans / gender nonconforming person (especially transwomen, the most marginalized members of the LGBT community) will be seriously hurt or killed.