Back when I was in M&A banking and working insane hours, the only time I saw new faces were at industry conferences (where everyone is in hyper networking mode). There, the most successful tactic that actually resulted a dozen or so dates was when I hand-wrote on the back of my business card "Smile if you'd like to join me for drinks after this. KC"
When she cracks the inevitable smile, I give her an evaluative look and ask "Should I take this as a 'yes?' "
Expressing direct interest? Check.
Makes her smile? Check.
Unusual/memorable? Check.
Nonthreatening? Check.
That said, this is a tactic that is congruent with my goofy/offbeat personality so YMMV.
I was consoling a friend, who'd just been kicked out of his house and his company by his wife. We were sitting in this little place that tried to be a restaurant and tried to be a sports bar, but it closed at 9:00PM, so it sort of failed on the sports bar part.
Anyway, it was rising on closing time, and this waitress, clearly ready for the end of her shift wanders over to us. I'm trying to be witty and funny, and get this guy laughing.
I say "Miss, I notice that you have a sign that says 'No shirt, no shoes, no service'"
She says, "Well, yes, that's the health code."
I said "And I can't help notice that you're not giving us any service, and you're also not wearing shoes. I must insist that under the health code, you remove your shirt at once"
My friend bursts out laughing, and says "I"m a health inspector, I'll take it from here. Miss, if you would step over here with me for a full inspection..."
I made him laugh. They left together. It's all good.
My friend (Dean) and I headed to a club a few years back and it started to rain (Fall in the Northwest). As we get around the corner there is a huge line to get in.
Dean: Screw waiting in line Me: Yah, I'm sure we can give the bouncer a few bucks and get on a list
As I'm saying this he's taking off his jacket and walking to the front of the line and goes to a group of girls close to the entrance where one of the girls was shivering
Dean: Hi honey I got the jacket from the car for you... Girl: Huh...thanks...(she smiled and they started chatting) Bouncer: How many Girl: All of us (pointing to her friend and us)