Attenuators should work for both guitar and bass amps, AFAIK, they only regulate the signal being sent from the power amp to the cab.
However, they should only be used on amps that have a Valve driven power amp section. A quick Google search of the Mesa TT800, shows that it's a Class D power amp, so therefore you don't actually need an attenuator. The TT only has valves in the pre-amp (3x 12AT7).
The attenuator works to maximise the signal into the valve power amp, but reduces the signal into the cab, without damaging the transformers & power valves in the amp. It allows the power amp to be driven into distortion, which is a smoother and clearer sound than pre-amp distortion, which is "spiky" and can make the sound somewhat "mushy".
Basically, you don't need an attenuator unless you're using an amp with a valve power amp stage.