If your are using the Bitly API, you should no longer be using your API key. Instead, you will want to grab your Oauth Access Token, which you can find here when logged in to Bitly: https://bitly.com/a/oauth_apps
Some third party apps, like Tweetdeck, still ask for your username and legacy API key. To find your username and API key, you can visit this page while logged in to Bitly: http://bitly.com/a/your_api_key
To reset your API key, sign into your Bitly account and go to 'settings' located in the top right corner drop down menu. Head to the 'advanced' tab and scroll down. Click on 'show legacy API key', and press the 'reset' button.
You can now use this new API key.