[QUOTE=. she’s always overjumped things when she felt like it, even a tiny cross rail. she went in this bit before:
[IMG]http://i271.photobucket.com/albums/jj131/gymangel812/20150330_141115_zpsuqitbug9.jpg)
the bit was changed because she needed more brakes (long story short). my trainer suggested the current bit, which improved our brakes and i had to yank on her mouth much less. i don’t really want a stronger bit, i would like to try a different one and see if it helps.
she rushes with my trainer also, so i’m not sure it’s a rider issue. my trainer is saying the reason she rushes is that she’s excited and likes to jump.[/QUOTE]
There’s a lot you can do with a green horse to teach them without going to stronger bits. But if you really feel you must bit up your horse. I’d suggest trying a snaffle gag with two reins. I’ve only used the single jointed type, but there are french link versions out there if you can find one.
http://www.adamshorsesupplies.com/centaur-stainless-steel-cheltenham-oval-mouth-gag-204394?fee=1&fep=38188&gclid=CPOAtvDKtscCFUyPHwodSMoHsA
The mouth feel should be familiar for your horse, but the gag action can be very effective when used in the right hands.
I like this bit as a training bit for horses that get strong. I ride off of the snaffle, and for the most part it is a simple snaffle bit. But when the horse misbehaves you can engage the gag action to the degree necessary to get the horses attention and get them listening again.
As a training tool this bit is nice because once the horse is listening to the snaffle, you can put the gag bit away and switch to a regular snaffle.
This is my go-to bit for saying ‘hey listen up’, and they get a very obvious reward when they do listen.
Use this bit only on horses that can tolerate this type of gag action. In the wrong hands this can be a dangerous bit because the gag action can be very severe, so don’t uses it if that makes you uncomfortable.
I think you sound like you’re doing lots of appropriate groundwork with her. An exercise I’d recommend that I think helps a horse to listen:
(I also think you should try this exercise first in the bit you’re using now.)
Set up a pair of ground rails on the long side of the ring, and set the distance between so you can fit in either three long canter strides, or four short short canter strides. Then practice lengthening and shortening the canter between the rails until your horse is listening to your half halts, and the horse has the exercise down pat.
Once you’re comfortable, set jump standards at the ends of the last rail and leave the rail on the ground, practice with that set up to get the horse used to it.
Then make the last jump into a small cross rail with a ground pole at the base (adjust the distance between rails as is necessary), and see how the horse reacts. Practice getting in the three strides or the four strides before the cross rail until the horse is listening.
Then you can incrementally raise the jump if the horse remains comfortable and listening.
The nice thing about this exercise is that you can add a placing rail in front of the jump to help the horse find his distance. If all goes well you can eventually transform the whole set up into a gymnastic of your choosing.
I like this because it helps the horse learn in a step by step fashion, and you’re not over facing him with anything all at once.
But definitely mix it up with other flat work and exercises to keep it interesting.
Good luck. 
Edited to add: I just wanted to say again that the snaffle gag is not a bit for inexperienced riders. To use it correctly a rider has to be experienced riding with two sets of reins with dexterity. Applying the curb rein to put pressure on the gag is an art in itself. This is a bit that most would not use on a green horse unless they knew how to use it. It would also not be my first choice to use this bit as there are other training methods that should be tried first.
I’m only mentioning it because you specifically asked.
I hope you understand the rational I’m using for suggesting the snaffle gag. If you only connected the snaffle reins to it you would essential have a regular mild snaffle bit on a green horse. But by putting the curb reins on it you turn it into a powerful gag bit, that when used with experienced hands, can make a powerful training tool. But this is not a bit I personally would ever use as a permanent bit to ride in. I consider it a training tool only.
If a rider using a snaffle gag ever lost control of the curb rein, and it caught on something, or the horse stepped on it, things could get really ugly.