Meaning a shit load of rum. Hence, the word bath in this word refers to bathroom, which is connected to 'shit load' and rum which is referred to the alcoholic beverage.
This exists also in the Junior Suite at the Davitel Tobacco Hotel in Thessaloniki, Greece.
Jay: 'Homie, we need some pre-drinks before we hit da club! There's a liquor store on da corner, leggo...!'
DeShawn: 'Don't worry homie, I got us, i got a bathrum! BRAP, BRAPPP!!!'