At the moment we don’t have a plug & play solution for that scenario, but it is definitely possible to build with a module. Commerce ships with a scheduler that could be used to schedule an automatic check when an order is placed. That would check if it’s a manual bank transfer order, and then sends an email automatically after a certain time.
We could probably put together a basic module for this in just a couple of hours if you’d want to commission it for your project.
I have also made a note of the idea in our tracker, would be fun to work on it whenever I find some free time to build something new…