After reading Converting Hg repositories to Git directed me into reading Bitbucket: Converting Hg repositories to Git I hoped moving my Mercurial repository on BitBucket to a Git repository would be something like following the steps.
First of all, hg-git on a Windows system requires Python or TortoiseHg. Neither of these I wanted to install for a one-off conversion.
So I took a throw-away Linux VM, and did the steps below. But let me first explain why.
My motivation for moving away from BitBucket to GitHub, especially for projects containing markdown documentation.
When writing documentation in Markdown, being able to in-line reference pictures or have relative-references to other documents. This works perfectly in local Markdown tools (like MarkdownPad 2 or LightPaper).