Copado Essentials now supports connecting to Bitbucket repositories, in addition to GitHub. Connecting your Bitbucket by using your normal sign-in, is similar to how you'd connect your SF orgs, Github repository, etc.
When you add an org, simply select Bitbucket in the Type dropdown. Give your repo a name and proceed with authorization. Upon successful authorization, the Git Repository dropdown will list all the repositories that you have access to. Select a repo, click Save and you should be ready to deploy from and to this Bitbucket repository.