After coming across this stackoverflow post: http://stackoverflow.com/questions/913912/bash-shell-for-windows
I discovered Console: http://sourceforge.net/projects/console
And I can use it with the Git shell, setting the shell to:
"C:\Program Files (x86)\Git\bin\sh.exe" --login -i
Just amazing!
Update 2017/05/04: The original project is no longer active, but this fork seems to be: https://github.com/cbucher/console