Go to the Tools menu and select Add. In the Name entry field, enter something like 'bash prompt' and in the Command entry field enter start bash --login -l
and check the "Don't show the command output window". This will add the following config entry:
[guitool "bash"]
cmd = start bash --login -l
noconsole = yes
This gives you a "Tools\bash" menu item to click which launches your bash prompt.
Note that due to the 'start' command prefix, it is independent of the launching Tcl application and will stay around after you exit git gui.