So you want to approach, coming across as NOT approaching? Do you pay something without actually giving the money

same thing.
Let me ask you something: are you embarrassed of being a man?
If men wouldn't approach women and vice versa, humankind would simply become extinct..and since it's VERY socially accepted ( I prefer saying socially PROGRAMMED) for the man to make the first move - it's your NATURE as a man to approach.
So why are you trying to apologize to yourself for being a man? Go to the mirror right now and say - sorry dude, you're a man..and you can't approach women because it's approaching women. It's BS. It's your NATURE to approach, so never ever feel ashamed about it no matter what outcome, whenever. You are doing what you were born to do - frankly, to make sure humankind survives, lol..but you were invented for it remember
99% of the men tell a woman they're sorry for approaching her: oh sorry! I didnt know you had a boyfriend/bad night/blabla...or "I just want to have a drink with you, nothing else." Show some guts, look her straight in the eyes and tell her: "you have a bf? I understand. Now lets go grab ourselves a drink, come on! It'll be fun" or...if you REALLY have some balls on ya: "you have a boyfriend huh? Well congratulations! That must be a major accomplishment for you

but where I'm coming from? Ït's quite common." It's ridiculing her objections...but it's to prove my point: NEVER apologize for being a man, go out there and APPROACH...who cares that they know?
It's that they SEE and SENSE that what you're saying is far from friggin' genuine, that you're faking something, that you FEAR they'll "expose" you...for what? For being a man? Now go out there and approach with confidence, fearless, indifferent to the outcome...you were born to do it, so NEVER apologize for it in your own mind!
I even go as far as when she asks if I approached her I said nahh...you know how I usually approach women? Then I walk away, come back and act all stutterish, exaggerate nervousness, Im fidgeting around, talking about how I invented Microsoft - the whole acting scene will make her laugh out loud, and it immediately lets her know that you're NOT a wussy.
That's your sticking point: you fear how you will be perceived if you approach, which is approval seeking onto itself..be indifferent and never apologize - realize you are SUPPOSED to do it.