How about a line that doesn't talk about yourself or who you are, but suggests something that your new acquaintance might want to join you in doing:
Let's throw a potluck!
Please invite me for a bike ride some time
Want to go swimming?
Just pick the thing that you most want to start doing with new people and write a call to action around it.
Love this! The possibilities are endless, especially if you consider the inverse:
Don't call me to go to the mall.
Don't call me to eat at a fancy restaurant.
Don't call me for advice on what new sports car to buy.
No, I will not help you install the giant TV you just financed.
No, I will not attend your pretentious destination wedding.
Fun!