you gotta go out more, if you are in a bar the whole damn venue is there for socializing, there is nothing special you have to say or do, if you are getting approach invites go approach with intent knowing that a girl already gave herself away before your approach, if no approach invites, you can approach all the same, what you say means very little (although saying certain things creates certain frames, and different frames support different functions)
the mind frame from which you are expressing yourself and how you are feeling and processing information, much more important then ''what'' you say, is ''how'' you are saying it, and why you are saying it in that way in the first place
from a personality point of view, confidence is your best friend, that is certainty, if you need 3 hints that a girl is checking you out just to go talk to her, then it would be interesting to see how congruently you can act in a way that seems confident and manage to escalate
to much worry about what will happen, and what is right and what is wrong, how to not lose and what to do, this all comes from a needy place
you have to channel your energy into a focus, be sure of what you want, what the girl wants and what you want are not the same, pay attention to how she feels, but what you want is #1, forget about her priorities, there are other girls, if what she wants is not in alignment with what you want, then you most likely have no chemistry and it's not important for you to impress her anyways, better to just move on and let her compromise for you, if she doesn't who cares, there will be better girls out there that possess what you are looking for in a partner, you just have to find them, go out and find what you were looking for, figure out who you are, display your personality, get to know her, see if she is what you are looking for, if not move on, if she is, move forward
TL:DR
doesn't matter, how you feel is more important, just know that she is into you and you want to talk to her, walk up and just say what's on your mind, say exactly what is in your head and what you feel at the time, be absolutely 100% honest
if you were to pick an opener that most likely expresses your frame congruently from your original post,
Quote:
Say a girl is giving you long glances and is checking you out while she's on the dance floor or at the bar. How do you approach them?
you would open with something like:
hey, I saw you over there and thought you were checking me out, who are you?
then take it from there, no plans per se, but rather an idea of what you want to do, just doing as you please and expressing exactly what is on your mind from moment to moment