Use Github Windows client with Bitbucket
Create your account with Bitbucket and Github, if you haven't already. Then, within Bitbucket, go Avatar > Manage Account > Connect Accounts and choose Github. Do whatever it says, then create a repository.
Open the Github Windows client and create a new repository. Move your files into this new repository. Make an initial commit, then close the Github Windows client.
Find the repository folder and, within the .git folder, find and open config. Add the following new lines, replacing the relevant terms:
url = https://email@example.com/bitbucketusername/repositoryname.git
fetch = +refs/heads/*:refs/remotes/origin/*
remote = origin
merge = refs/heads/master
Save, and open up the Github Windows client again. Now hit Publish and you should be prompted for your Bitbucket username and password. Done.
* This is the quick and dirty way, avoiding SSH. Sorry.