That would be fairly easy to do with UPB.
There are a couple of options, but the easiest would be to get a small UPB tabletop controller, a UPB switch and UPB appliance module (not required, but will make it all work seamlessly). Replace the bathroom switch with a UPB one and the outlet the hood is plugged into with the UPB module. Program the tabletop controller to turn on the module and switch.
The module is not required, but you would have to manually turn on the hood and the switch separately. So 2 button presses instead of one.
Please do not send me PM's asking for software! You will not get it.