Accessing a remote Windows "Git Bash" prompt from a Linux machine?
Solution 1:
As far as I know, PowerShell lets you use SSH to log in to the Windows box remotely to access the command line shell...
EDIT I found this PowerShell server (free for personal usage with 1 connection)
Solution 2:
All you need is an ssh server that allows you to define your startup.
For example, freesshd, then set the command shell to the same as your normal git bash shortcut would set it, ( C:\Windows\System32\cmd.exe /c ""C:\Program Files\Git\bin\sh.exe" --login -i" ). Since freesshd can run as a service you'll always be good to go.