You need to export your issues from Bugzilla, and then use the GitHub API to upload the issues into GitHub:
http://developer.github.com/v3/issues/#create-an-issue
(note that the old issue-import through GitHub support channels is discontinued)
This does mean your issue numbers will change, so you might want to append a 'Bugzilla-Id' footer to your issue description, so you can use GitHub's free-text search on issues to find them from the old Bugzilla ids.
As far as exporting your data from Bugzilla goes, I think your options are:
Good luck! If you do write an export script, I'd encourage you to open-source it on GitHub!