My favorite riding competition was dressage. I never really liked the jumping competitions, although I did them quite frequently. In dressage I usually felt more strongly connected with my horse than at jumping. Doing both I was very familiar with all kinds of dressage/combo bridles.
First I have to make clear that the dressage bridles are absolutely perfect for jumping competitions too. You have today so many choices of dressage/combo bridles that it might overwhelm you. Here are some points that could help you choosing the right one for your horse or pony.