The bill will be in dollars. Yes, you can use cash dollars as part payment. You'll need to settle your account before you depart the ship and as quite a few passengers preferred to settle by cash, if you left until the last minutes, the queue can be horrendous at the info desk. ie they operate the cashless system onboard. The last night before you leave the cruise, you'll receive a statement (you can alsoview your account via your room TV),thenyou 'll settle the bill at the info desk.
The dollar rate is fixed throughout your cruise so no surprises, you can chose if you want to convert to dollars on your credit card bill or in sterling, you can use dollars directly into the machines in the casino and I believe you can also pre-pay in dollars at the beginning of your cruise.