Your top bet is to ask your real-world friends. If you don't know any Dribbble players personally, check in with your web industry pals—they may have a friend who can hook you up.
Many players obtain their Dribbble invite by tweeting out that they're looking for one, an excellent tactic if your followers are familiar with the quality of your work.
You can also keep an eye on your feed for invite giveaways — players will often make an announcement on Twitter when they have fresh invites.
If you can't squeeze an invite out of your friends or followers, try a proactive approach and maintain Twitter searches for invite giveaways. Keep a link to your work handy to jump on these opportunities as they arise.
Patrick Haney runs a great group over at Flickr dedicated to finding talent to draft to Dribbble.
“All you need to do is run some drills during our try outs, and the players with the most potential will get drafted. ”