Bitbucket allows you to reliably track all changes and updates to your code base, merge requests from different teams, and easily roll back changes while making your repository available to your entire team. To start pushing files to Bitbucket, create a new repository by logging in, clicking the plus button, and selecting Repository. Note the repository URL and navigate to the folder you want to sync using the command line. Use `git init`, add the local files with `git add .`, check the Git status, make the first commit with `git commit -m "first commit"`, and finally push the folder contents to Bitbucket with `git push origin master`. Once authenticated, the upload process will be complete, and you can verify its success by opening the repository in your browser.