First, sign into your account:
1. Sign in via your Twitter or Facebook account
2. Use your email address and password associated with your account.
If you signed up with Twitter or Facebook, you would actually use an opaque ID that was created when you signed up for your account. This is technically your username. Some 3rd party applications ask for your username and API Key to connect with Bitly.
You can find your username by going to your Public Profile on Bitly. Do this by going to 'Public Profile' located in the admin panel drop down.
Take a look at the hyperlink URL located in your web browser.
You'll see something that looks like this:
In this case, 'o_5ivagqtvj9' would be your username for these other apps. You never need to use this username to sign into bitly.com, but other applications may ask for it.