I believe the source not bit.ly will show up as the referrer. IMHO, the best way to track shortened links back to your site is to use the Google Parameters. Not sure if bit.ly offers a way to do this easily (Hootsuite's shortner Owl.y does)

Even so, you can add the params yourself.

So if I tweet out about a blog post on my site, I'll put this kind of link into the shortner:

www.mysite.com/postname/?utm_source=twitter&utm_medium=referral&utm_campaign=mycampaign&utm_content=title-of-post

Then I am sure to be able to see my "campaign" info in a variety of ways inside of GA.

Hope that helps.