Should I be worried about sensitive data being leaked?

If you’re not exposing any services over the internet…no?

Can you elaborate on this a bit more because I’m trying to figure out where you would arrive at that conclusion that it would be possible. Perhaps there’s something in your setup that you haven’t explained fully.

Could it be as simple as grabbing a docker image and running the VM inside a container?

That’s not how docker or VMs work.