It's too easy for a dealer and a player to cheat. If I was a floor supervisor I wouldn't want my dealers being more than friendly with their players, "Be friendly but don't be friends" is how I would look at it and for good reason, look at what happened with the Tran Gang. With that being said, some houses are more lenient than others and it doesn't hurt to try.
There are several approaches that are considered effective when it comes to asking someone out. I would just say, "Hey, what time do you get off work? We should grab a drink." Some people prefer to take a more direct approach though, and there's nothing wrong with that. One of the more mainstream approaches is called "doing the Donald" which I hear is very effective if you're a super star. I would stick with the tried and true "Hey, what time do you get off work? We should grab a drink" approach.