Since you said you were jumping her, I would think you are riding the horse English. Curb bits are not designed to ride with any kind of contact. The reins are long so they can have a nice curve at the bottom and be ridden super loose.
If teeth issues are ruled out, then I would guess she does not like contact in a bit that is designed to have very little contact. The slightest movement of the wrist (1/4-1/2") creates enough contact in a curb to tell the horse to slow down or drop their head. Expecially if the reins are weighted (double stitched and doubled over leather for at least 6" from where they connect to the bit) they give tiny cues and are better used for neck reining.
If you are wanting to ride with contact (and shorter reins), I would totally agree with getting a mullen mouth, a 3-piece snaffle, a regular snaffle, a side-pull, a hackamore, or continue using the halter. There is no written rule (that I know of) that says you can't ride in the whatever the heck you want. haha. I know people (much braver than me) who ride tackless on the trails and their horse is totally tuned in and they feel safe. When I was young and I bounced, I rode bareback in a halter everywhere except lessons and the show ring. Was it safe? Sure! I survived. lol. Keep yourself safe and the horse comfortable.
One last thing to consider is that while you are riding the horse and keeping her exercised, she does belong to someone one else. You don't want to undo anything they have done. You don't want to change the horse they bought for whatever reasons they had, into something that no longer serves the purpose they bought her for. If they wanted a horse they could hop on once a year in a standard western get-up and take off on a trail ride and you ride in completely different gear that changes the way the horse responds to the gear the owner is comfortable in, there can be an unintended problems. That being said, for your own safety (and comfort), it's always smart to have your own gear and clean it well between horses.
If teeth issues are ruled out, then I would guess she does not like contact in a bit that is designed to have very little contact. The slightest movement of the wrist (1/4-1/2") creates enough contact in a curb to tell the horse to slow down or drop their head. Expecially if the reins are weighted (double stitched and doubled over leather for at least 6" from where they connect to the bit) they give tiny cues and are better used for neck reining.
If you are wanting to ride with contact (and shorter reins), I would totally agree with getting a mullen mouth, a 3-piece snaffle, a regular snaffle, a side-pull, a hackamore, or continue using the halter. There is no written rule (that I know of) that says you can't ride in the whatever the heck you want. haha. I know people (much braver than me) who ride tackless on the trails and their horse is totally tuned in and they feel safe. When I was young and I bounced, I rode bareback in a halter everywhere except lessons and the show ring. Was it safe? Sure! I survived. lol. Keep yourself safe and the horse comfortable.
One last thing to consider is that while you are riding the horse and keeping her exercised, she does belong to someone one else. You don't want to undo anything they have done. You don't want to change the horse they bought for whatever reasons they had, into something that no longer serves the purpose they bought her for. If they wanted a horse they could hop on once a year in a standard western get-up and take off on a trail ride and you ride in completely different gear that changes the way the horse responds to the gear the owner is comfortable in, there can be an unintended problems. That being said, for your own safety (and comfort), it's always smart to have your own gear and clean it well between horses.