What types of exercises can I do to help rebuild my confidence when jumping?

Lots of simple work in indoor arenas where there's a controlled environment. Just doing lines of small gymnastics.
Doing simple exercises, like 1 jump with a ground pole at 4 strides, in this case, you don't have to worry about the distance. Start with low hights and enjoy it :)
I would also suggest doing lots of ground pole work. That way you can have confidence in your eye for distances without having to worry about an actual jump.
I agree with Norman about going stirrupless at all gaits, even bareback at all gaits. Practice calm, smooth transitions with you sitting tall in your seat, quiet aids. Another idea is to put a grab handle on the front of your saddle (also known as monkey handle, etc). When you feel insecure, you can grab the handle and use it to push yourself deeper into your seat. Good luck! :)
I suggest a lot of 2-point and no-stirrup work at all gaits. Get your instructor to help you fix your position in it :)
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