It turns out that you can use Bash on Windows 10 to run X applications, including through ssh tunnels. Here’s how.
First, go and install XMing. I’d strongly suggest not allowing it to get access to your network, so it stays on localhost. This is so that an attacker can’t draw stuff on your screen through your X server.
Run XMing, put it in your startup if you want. You now have an X server. Next up, you’ll need to fire up Bash on Windows, and run
sudo apt-get install xauth. Then edit your ~/.bashrc . Right down the bottom, add the following;
export DISPLAY=localhost:0 xauth generate $DISPLAY
This causes your session to be configured so that you can use X applications and they’ll be pointed to your X server. It also provides the correct X authentication tokens to make things like ssh work.
Now, log out and back in again. Start up Bash for Windows, then you can run stuff.