The problem is that each of your desciplines have different requirements and different bits are considered correct. I would guess it is the jumping where you need the most help?
I tend to stay away from any bit that has a harsh mouthpiece. You will never find any wire, twists, waterfords, etc.in my tack room. However, I may have some bits with poll pressure. I have a Dutch (bubble) that I will occasionally use with two sets of reins. I also have a full cheek gag bit (not as bad as it sounds). These bits work by adding pressure to the poll nerve to get the horse's attention.
On a couple of my event horses, I have used a kineton noseband. This is a good tool for pullers. ::: Sustainable Dressage - Tack & Auxillary Equipment - The Bridle & the Bit :::
While I will agree that training can be a cause, it is not always a fix. I have ridden many extremely difficult event and jumping horses that were just too full of themselves. If you think you can undo some of them, have at it!!