CI/CD pipeline automation from AEM on premises to Cloud?

Have you tried integrating Bitbucket and ran into any specific issues? 

Easiest standard pattern is to leverage Adobe Github. You remote sync, ship your code from your Bitbucket into Adobe github and run cloudmanager from adobe github. Documentation. 

But for this, code must be shipped from Private repo into Adobe github repo. This can be done using Jenkins or Github Actions workflow. 

Another approach is, adobe now allows to add External Private repositories into Cloudmanager. Documentation. There is a specific documentation for Bitbucket users, to setup webhook from Bitbucket. Step wise instructions with screenshots. 

Please follow the documentation. Can help if any hiccups.