It’s not possible to send “pull request” across different sites today. I’ve added a feature request for this in the Bitbucket issue tracker: #3288. I suggest you add yourself as a follower if you want to track this.
However, you can still move the source from GitHub to Bitbucket without having to download any zip files or tarballs. You make a clone from GitHub and push to Bitbucket:
$ git clone https://github.com/cakephp/cakephp
$ cd cakephp
$ git push git@bitbucket.org:mg/cakephp.git master
I created mg/cakephp as an empty Git repository in Bitbucket first. That way you can push/pull changesets from GitHub to Bitbucket.