Recommended way of authentication.

How do I find my oauth access token?
Please go at this url https://bitly.com/a/oauth_apps

Click on 'Generate Token' button.

If the button 'Generate Token' is disabled, most probably your email address isn't verified yet by bitly.
You'll have to verify it. Your email address must be verified before you can generate your access token.

Configure your bitly account in the General section.

Deprecated way of authentication.

How do I find my API key?
Please go at this url https://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.

Configure your bitly account in the General section.