Tim....bottled water is sold in small bottles....litre bottles....half gallon ...gallon....and 5 gal bottles.
I don't think you need to bring the Brita.
The ice companies here use purified water to make ice....so don't ask the bartenders if the ice is OK to drink....LOL....they get asked that 50 times a night.
Most resorts and restaurants use bottled water for drinking and preparing food.
I don't think you will have a problem.