Try a ported or a curved forward bit. Also often a thinner bit can help as sometimes they are putting their tongue over the bit when they have a very fleshy tongue.
Get someone/your instructor to watch what happens when you ride, and whether it happens at certain times/movements.
You could also try a drop noseband if none of the above work, but from my experience it is often a contact/space issue.
As suggested above, trying a ported bit helped with my cob. Very fussy in his mouth, and I tried so many bits that should have been softer, kinder, take less room etc. Full cheek Myler was best of the bits I got recommended... Until I tried a pelham hacking- and he loved it. Have now discovered that he's best in a chunky happy mouth eggbut - fussy prob once a year instead of every ride, and he wears it for everything.
So much for a nice loose ring NS or hanging cheek with plenty of room for his fat cobby tongue!
One horse here was dreadful. He had his tongue over the bit (a French Link) more than he had it under it. He would flick it over and under 5 or 6 times a minute. His owner changed him to an HP Relief barrel bit and he stopped doing it on the first ride. He has a really quiet mouth now. She had tried all sorts of bits with him in the past as well, including some very expensive ones. Only your horse can tell you which bit he likes. Daft question, but you have had his teeth done?
The best cure is to find a bit he's happy with so he doesn't want to do it. It took 18 months and about 40 bits (really not exaggerating!) with my horse when I first had him as he'd be ok for a week or so, sometimes longer and you'd think you'd cracked it and then he'd start again. Trial and error is the only way I'm afraid. The flat work bit was fairly easy (about 6 months and about 8 options) but didn't give me enough brakes for anything else and finding a stronger one he was happy with was a nightmare! 9 years on we have 3 bits - a Myler Mullen mouth hanging cheek for flat work and quiet hacks (90% of riding these days) . A Waterford hanging cheek for more exciting hacking or if someone new is riding him (just in case!) and a Waterford 3 ring gag with 2 reins for really exciting stuff - he had this for jumping when he could jump, now reserved for fun rides. I was wary of the Waterford but it's a mouth piece he really seems to like, I think he likes the flexibility of it. Jointed bits, even with a lozenge, were the worst for him.