You know, it's funny because when I think of "approaching," I think of going up to a dude and being like, "Hey, I'm Bunny77. What's your name?"
And I'm thinking, no way jose... I'm not doing that!
But I definitely think there can be some strategy in not being that direct, but positioning yourself. Like you said, dudes love to think it was their idea and YOU were the one who plotted it all along.
My best example of this was seeing a cute guy at a basketball tournament and I really wanted to meet him. So I made friends with his friend and sat near his friend. When dude came over to talk to his friend, the friend introduced us and he was like, "Wow, who is she? I didn't know she would be sitting here!"
Ha ha ha ha ha.....He ended up inviting me to dinner with all of his friends that night!
(Bad news is that he had a girlfriend, but in terms of getting a positive response, it worked!)