We have seen about everything down here. Harry is correct, you can bring booze into your room without issue - Coco has fridges in the rooms, so that would seem to back up that concept.
As for bringing "your own drinks" to any bar is in general frowned upon. Same with bringing food to a restaurant, just not a really proper thing to do. But also as Harry says, it is fine with some places. For instance, if you are a Tito's Vodka fan, you are unlikely to find that at most bars. So just let the bartender know that you would like to have your Tito's, and you will buy the glass and mixer from them.
Same would go for a Budwiser drinker, you can stock up at Mega Mart (or HiLo) and then ask the bartender if they dont mind if you drink them instead of the local brews. You can even ask them to store the Buds in their fridge and then order them and tip the bartender for their service. These are the best ways to drink what you want when the bar doesnt have it in stock.
