The biggest risk I see, besides attempting to carry-on bowling balls, is choosing what equipment you are going to take without seeing the patterns.
IMO, check your equipment it will be fine and you won't have to leave any accessories behind either.
At last years Nationals, I took 4 balls (3 + plastic). I flew SWA and checked 2 bags: a 3 ball roller with 2 balls in it and a 2 ball duffle with 2 balls. I pack my clothes and all other items, between those 2 bags and a backpack carry-on.