Mister Big,
I see what you are trying to get at with you buying the drink and ignoring her thing. You are letting her know that you find her attractive, but you are not going to be like every other guy out there and come hit on her after the drink has been bought, you want to be different.
Now, that will work sometimes if she finds you at all attractive. But, what about the times the girl just thinks that you are too much of a loser or too shy to come over and talk to her-and that the only way you can initiate anything is by doing the old stand by drink thing? What if she thinks wow, hes cute, but he must be a social retard to think that I am then supposed to come over and hit on him just because he bought me a rum and coke? SO, it could work, but its a double edged sword imo.
Now, if it is truely like you say it is and you dont really care if you talk to her or not, then thats fine. But if thats the case, then why do you do it for the girl you find most attractive in the entire place? Deep down you must care if you pick out that particular girl to buy the drink for. Why dont you do it for just an average girl (in your opinion) and see what happens?