Part of customer service ettiquete is to be friendly to customers and very smily to customers , however you may be in for a chance and theres only one way to find out !
I know you've mentioned the bar is rather busy but if there are any peaks and troughs in busy times these would be your oppurtunities . Ask her a few questions bout herself , try and inject the conversation with humour and then casually drop in , sooo when are you free ? / what are you doing after work / would you be up to go out some time etc . If she likes you then she will be happy if not she will probably reject you in the most polite way . Good luck ! Dont pass up the oppurtunity mate