How to keep my balance on a bumpy horse?

I am a fairly new rider, and since the Yahoo answers community has helped me a lot before, I believe it could happen again. But anyways, I ride a pretty bumpy horse Western style. And a lot of the experienced riders think so too, so it's not just me. Unfortunately, I have a terrible sense of balance, and whenever I let go of the horn, I fall off. I know! Really bad habit to get into, but I just can't help it. I really want to let go, but I want some tips to help me stay balanced. I don't want to lope before I can trot without holding on to the horn. I've actually loosened my grip a lot since I started, but that doesn't really seem to matter. I've tried "moving" with the horse, but it's truly hard for me to do on a horse that has a very choppy gait. My old trainer tried to get me to do a whole bunch of stuff that I wasn't ready for, and I told him that I wasn't comfortable enough to do that yet. But he told me to do it anyway, and it resulted in me falling every time. I don't know, maybe I'm just not a really good rider. But I think I'm just afraid that my taking any risks will make me fall. And I know that will just make my confidence go down even more. So I really want some good tips. And this is coming from someone who's kind of being reintroduced to riding, and the introduction wasn't so good. And I'm truly kind of scared. I know I'll get answers saying I shouldn't be, but I can't help it! I wish I could just pick up the courage to take a chance. But that's just not how my brain really works. So please, some good tips for a scared beginner. I love riding now, it's basically my life, but I know I'll love riding a whole lot more once I get better. This would be a huge step for me, so please help.