At least in eventing and local shows, I have found that it is totally ok to use a close contact saddle if you do not have another saddle. I use my CC for dressage all the time. It's just hard because it doesn't put you in the right position.
Dr. Bristol bits are approved, from what I understand
You CAN show in a CC saddle. I do, even at the one rated show I did! But you should consider what your priority will be, dressage or jumping. (assuming you have a CC b/c you jump) Use what will be most beneficial for you. I do dressage to help my horse's jump better and give them time in the show ring. At this point in my life I don't care if I never master a piaffe and I don't care about the looks I get in brown tack! But if I really wanted to be serious about dressage I'd invest in another saddle.
I think Dr Bristols used to be illegal but were recently legalized? I'm not the one to ask about that... a rule book should say somewhere though!
Dr. Bristol bits are illegal at nationally rated shows. Events sanctioned by other groups (ie not EC or USEF) may follow different rules. Check them.
In compettions sanctioned by the FEI, "dressage type" saddles are required. Again, check the rules of your sanctioning body.