I hadn't thought about that (I use PowerShell for most tasks so that is still my "home" shell and it's bash that's the rare one), but I half remembered something to that effect, so I went to the docs:

https://docs.microsoft.com/en-us/windows/wsl/interop

Calling Windows EXEs from bash will automatically retain the current working directory under /mnt/c/*, so it should just work out of the box. Looks like you might be able to get away with just adding native Windows git to your bash path.