To use your Bitbucket repositories with Release, choose the "Sign in with Bitbucket" option. You'll be prompted to authorize Release for your account information, settings, repositories, and webhooks.
Note that can you authenticate with multiple different source providers (e.g. GitHub and BitBucket). If you use the same email address for those providers, you will be able to see a combined view of repositories for all providers, and each integration will appear separately on your user profile page.