Yes, covering the walls would be nice, but not feasible. If I understand you correctly, a secondary ideal way would be to completely isolate the transmitter except for an "antenna" which could be chosen and adjusted at will until the range is optimal. Luckily, my experimentation with improvised low cost household metals seems promising!
Putting my $7 class II bluetooth "hands free" in a sauce pan with its cover on, reduces its range to about 1½ meter. Which is a way longer range than I had expected, but I suppose sauce pans are made of stainless steel and therefor not very conductive.
Covering the bluetooth hands free completely with one layer of aluminium foil, drops the range to about 50 cm (half a meter)! I think it is very promising that it did not block radio contact completely. The foil I tried with is marketed as "extra strong". Maybe there are thinner foils around. Or else maybe making some small holes in it could increase the range to room level. Two layers kill all contact at any distance.
I've also tried with steel wool (wire wool). When folded into an ordinary "sheet" of it, no contact was possible. Its flashing LED was still visable through it. But by stripping off layers, contact was achieved inside the same room but not in the neighboring room. This seems to be ad hoc scalable to any range from case to case. But dirty and a bit time consuming with trial and error. It seems to be very important that the cover is homogeneous. One open hole (say 1 cm diameter) in any direction relative to the receiver, easily makes the signal come through even to the next room. Somehow, bluetooth signals seem to manage to both penetrate through, AND reflect from, concrete walls!
I will have a look in shops what kinds of malleable metal grids I can find to experiment with. Maybe one could wind a metal wire around it?