In the Merge dashboard, head to Configuration and navigate to BambooHR. You'll then mark the check box "I'm a BambooHR partner and want my users to authenticate using BambooHR credentials in Merge Link".
Enter your Application Key, OAuth Client Id, OAuth Client Secret, and OAuth Redirect Uri you received from BambooHR.
Once you've entered in your BambooHR OpenID Connect partner credentials, the next time your users authenticate in Merge Link, they will be taken through the BambooHR OpenID Connect OAuth flow!