new.server> rsync -a -v -e ssh user@old.server.com:path/to/repository.git .
Make clients point to the new repository: Now on each client using the repository, just remove the pointer to the old origin, and add one to the new one.
cd path/to/local/repo
git remote remove origin # to get rid of the old setting, this was not in the BitBucket instructions
git remote add origin ssh://git@bitbucket.org/<username>/<newrepo> # modify URL as needed
git push -u origin --all # pushes _ALL_ branches in one go
git push -u origin --tags # pushes _ALL_ tags in one go
git clone --mirror <URL to my OLD repo location>
cd <New directory where your OLD repo was cloned>
git remote set-url origin <URL to my NEW repo location>
git push --mirror origin