Deleting recored shows

Nope, minis can delete from any TVs

If you have individual HDDVRs, even with a Genie, you can turn off remote deletion to prevent deletions happening from other rooms.

Any Mini Genies are Clients (extensions, not receivers) of the main Genie, so always can delete. Think of it as all those TVs on one box.

If you have the Genie-2 (HS17) it only allows Clients so there are no individual separation.

He wants to delete from only one room.

What is the receiver model of your Bedroom TV? As stated before, you can't delete recordings from one individual box unless the Bedroom TV is an HDDVR receiver

There is no way to allow only one TV to delete on all 7. You cannot block a box from deleting its own recordings.