Tyme2k makes good points.
I worry about this too, and I do think most (if not all) of it is "inner game." So, to lessen the mental embarrassment, I try to give adequate time between approaching women, but if you wait too long, you lose your "social momentum" or you may get too much in your head.
Personally, I find busy (and maybe hip?) bars the best. People come and leave a lot. People seem to linger longer inside clubs around my area (I guess because of the cover). I bet "street game" right outside of a club would be the best actually or walking up and down a strip of bars/clubs, but it's little bit too cold right now unless you're a smoker.
It may not look very "alpha" to go from woman to woman "failing," but if you talk with a woman for at least 5 min and have at least 2 min breaks in between, no one is going to know that you're "failing." It could just look like you know a lot of people and going around the bar talking with them. I was at a bar just a few weeks ago and thought that 2 people were good friends. I ended up talking with the guy, and he had just met her that night and was flirting with her. I had no idea.