Let me preface this by saying I agree with iridehorses. There is absolutely no substitute for face to face professional help, and I also would highly recommend you take lessons.
Now, PLEASE don't put a twisted wire long shanked curb on your mare. Those things are harsh even in experienced hands, and if you don't know what you're doing, you could do some serious damage to your horse's mouth.
Obviously a walking horse that is gaiting properly should not be throwing you up and down. From your description it's hard to tell if it's a balance problem on your end or a gaiting problem on hers. I'm just going to guess it's a combination of the two. I've only ridden a handful of walkers so I can't really help to much with how to fix her, but as for you...
The walking horse's running walk is four beats just like the regular walk. First you need to find your rhythm at the regular walk: count off the beats as each hoof hits the groud, relax into it and take notice how each stride moves your hips. Then do the same at the flat/running walk. The movement may be a bit more exaggerated, and the beat a little faster, but try to keep that steady count in your head and stay loose, allowing your body to move with the horse rather than against it.
Let me stress again though that there is no substitute for sound advice from an experienced horse person. You can read all the theory you want, but having someone there with you who can correct you the moment you make a mistake is going to get you a lot further a, lot faster than you'll be able to on your own.
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