Horses won't run themselves backwards unless for very good reason. It is a totally foreign movement for them, hence often used as punishment for some training matters - the horse HAS to listen to you as the hander or rider because they can't see where they're going and for all they know, could be able to back into a giant hole.
I'd be looking seriously for a pain response, get a chiropractor out, get your saddle refitted (by a professional, not a best friend down the road that knows a bit about saddles) and get someone experienced to check the fit of your bit and bridle.
When she backs up, are you pulling on the reins, leaning forward or gripping? By jumping off, you have very effectively trained her to go backwards when something is uncomfortable.
Once pain is ruled out, if she tries it again I'd be sitting very deep in the saddle, clamping my legs on (assuming this is an English trained horse that goes forward to the lower leg) and throwing my reins up her neck, while giving her a good whack on the backside, or a flick of the rein ends across its neck. The second she stops, pressure comes off and she gets to stand there quietly.
It sounds that you're not a hugely confident or experienced rider if you're jumping off when something goes wrong - maybe look at getting an experienced rider who will able to drive her forward without grabbing and getting scared, to have a few rides.