You don't have to bring your own and you are not to use the ones from your stateroom.
As you leave the ship there will be a large bin of towels (usually light blue great big towels) for you to take to the beach, but please make sure you return them. Sometimes they ask for you cabin number going and coming back, so if they are not returned they might charge you.
P.S. I believe if you want 2 each, they will give them to you. Will ask DD about this when I speak to her as she always goes to the beach and leaves the old folks on their own to shop.
They will allow you to take as many as you need. But please return them when you are done.
I can't say how many times I have seen HAL towels left behind because the user was too darn lazy to carry it back to the ship.