Use GitHub for Windows for both Bitbucket and GitHub

Is it possible to use GitHub for Windows for both Bitbucket and GitHub at once?

For example, can I have repo on both sites show up in the program, and when I commit/synch a repo, it push to the respective repo on the respective website?

No, if you mean: having a local repo with two remotes (one GitHub and one Bitbucket).
You can define only one remote with that client, and it will be either a GitHub one or a Bitbucket one.

Yes, if you limit to one remote, you can use GitHub for Windows with any upstream repo.

The process of adding an upstream repo is now easier with the (constantly) updated GitHub for Windows app:

select the URL and then drag the text from your browser, and drop it into the GitHub for Windows app. It will automatically add the repository.

(Original answer February 2013)

In order for "GitHub for Windows" to publish (instead of "pushing to GitHub"), you need to define a remote "origin" (in the settings of your local repo) using the https address of the Bitbucket repo:

https://[email protected]/user/repo

So if you create a local repo through "GitHub for Windows", you can add, through its settings, the right remote:

Note that the first refresh will trigger a login screen, in order for you to enter your http credential you are using on bitbucket.org: they will be cached (and encrypted) by GitHub for Windows for the duration of your current session.

(See "Password Caching" and "git: 'credential-cache' is not a git command", for more on that credential caching mechanism, recently introduced with Git 1.7.9+)

Any modification you are doing locally will be picked up by the GitHub for Windows client (you might need to exit the repo (left arrow in the top left corner of the GitHub for Windows client, and click again on your local Bitbucket repository: that will trigger a refresh):

The key in the next screenshot is in the word "publish" (instead of "push to GitHub").
That is because the remote "origin" is an https one.

Click on "publish" and you will see your repo status set to "in sync":

Rush to bitbucket.org to check if, indeed GitHub for Windows did push to Bitbucket:

There is also a new windows client that you can use with bitbucket. I tried it today and i think it is a better product.

http://www.sourcetreeapp.com/

There is now an even easier way to get GitHub for Windows to connect to your Bitbucket account. Check out the link below.

http://www.infragistics.com/community/blogs/david_burela/archive/2013/03/31/using-the-github-for-windows-app-with-bitbucket.aspx