Here's two examples of how you do it.
I'm at a wedding for a friend of mine, and there's this killer keyboard player. After the reception, I walk up to the keyboard player and say "I gotta tell you, as a bassist I hate keyboard players like you because your left hand is putting guys like us out of business". We shared a hearty laugh, and we start talking about the biz. After a couple of minutes, I hand him my card and I get his. Drummer overhears us, and gets in the conversation. I talk about how killer his ride cymbal sounded, after talking a little bit more we find out we both own music stores. Once again, we exchange cards.
I had nothing really to offer them, but some conversation musician to musician.
I'm at an open Blues jam. I don't know anyone there. I walk up to the signup sheet, and introduce myself to the guy running it. I ask him what style of Blues most guys play, West Coast, Chicago, or Memphis. From there we have a talk about the various styles of Blues and our favorite players. Next thing you know a few other musicians get in on the discussion as we take the conversation outside for a smoke. Based on the interaction from that night, I'll usually get called up early for a jam and get to play as long as I care to whenever I stop by there. I've gotten sub gigs from it as well.
Here's the hint that should help things.
Most successful musicians like to talk and network. It's how they got to where they are. I find more often than not, as long as I'm not sloppy drunk or obnoxious, they will talk to me. Because it's what musicians who gig alot do. They talk and network, and because of that they tend to be more receptive than people in other professions.
Also musicians tend to be passionate about stuff, and it's usually music. Find a point to connect that is something they are passionate about, and you'll get your in to a conversation.
But, like all things it takes practice. You may get snubbed, as I have. But, the many positive interactions I've received more than make up for the rare snub.
