After making eye contact at a bar, what should a guy say/do to start a conversation?

As a 21 year old guy who is not terribly outgoing and is new to the bar scene, I always feel insecure and nervous about approaching a girl I do not know but find looking at me from across a bar. I am not so worried about really carrying on the conversation and getting to know her (I figure this will either come naturally or it won't), but I really have no idea how to initiate this first time interaction without seeming like either a fumbling awkward guy or a creep whose only interested in pursuing sex.

Should just saying "Hi I am _____, what is your name?" be enough as long as I am confident? It almost seems too cheesy, and in my few experiences I feel like there was a better approach I'm not aware of to break the ice. On the other hand, offering to buy a girl a drink right away seems too direct, like I am only interested in pursuing a one night stand and have nothing else to offer, when really I am just trying to get to know someone for hopefully further dating. Also I have never been in a relationship and am inexperienced on pretty much all fronts of the dating world so any advice on the subject is appreciated. To make matters worse I am terrible dancer.

But anyway my question is, what is the proper etiquette at a bar to start a conversation with someone whom I've never met before? In your experiences what have been some of the most successful attempts to win you over early on?