Thanks for the suggestions, ya'll. My mare has got a very quick back up, and just like your mare, ImagineThat (named Candy? Too cool! XD) she ran into just about anything behind her. We ran into some bushes, and she still kept pushing back.
But my trainer taught my mare and I to back by pulling back with even pressure on the reins while putting some leg into her, and when we stop after backing I release the pressure of my legs and rein and she usually stops. When she's excited, she usually wants to go forward. She's never gotten my commands confused before, so it was quite startling. When I ask her to stop after having moved forward, it's usually enough to sit deeper in the saddle and say "whoa," and she drops her hindquarters into a good stop. When I ask her to move out, I give her slack with the reins and push her with my seat more than my legs, and when she tries to bolt forward the cycle just starts all over.
Also, NorthernLights and mom2pride, today I tried bending her in a circle, which helped to keep her from backing quite a bit. She still wants to bolt, so I have to stop her and she tries the backing thing again -- but if I put her in a bigger circle and work her at even gaits as ya'll suggested, I have a feeling that might help quite a bit. I wouldn't have thought of it, but it definitely sounds useful!
She's an absolutely wonderful mare normally -- I don't understand what's gotten into her. But thank ya'll very, very much for the suggestions; they'll definitely be put to use. C: