No worries- if the bias is set correctly the amp *should* have the lowest distortion for the class of operation it is designed for.
For example if an amplifier designed for class A is overbiased or underbiased, the distortion will be higher. There is a sweet spot. If overbiased, that amp may also be in danger of overheating.
Class AB amps are usually set up along similar lines, but with more emphasis on heat. For example in a transistor amp you want the output devices to conduct a little, so there are no switching artifacts (crossover/notch distortions). But OTOH you don't want them running particularly warm at idle either- else you will need a very large heatsink. At low volumes the driver transistors may actually be doing most of the work.
In a tube amp, the actual operating point might be a little less critical although you have to make sure that the dissipation in the output tubes is not exceeded as in a class AB amplifier the B+ voltages tend to run higher. So the bias has to be such that with the higher B+ voltages the dissipation of the tubes has a healthy margin. In addition, you have to have some concern about the balance of the tubes, as any mismatch in DC current for the power tubes through the output transformer can cause saturation distortion in the output transformer. So you have to be able to balance the tubes.
Not all tube amps have a provision for that- if not they are expecting that the power tubes be matched.
With respect to gain- bias will not affect that in the amp until you reach some sort of extreme such as cutoff in the tube or transistor. IOW, the output device has a certain amount of gain in the circuit that is dependent on its internal structure and the load impedance (also affected by any emitter/cathode degeneration that may be present). That is to say that with a certain voltage swing at the input you can reasonably expect a certain amount of output from the circuit, regardless of bias.
Now as the bias approaches some extreme like cutoff, you will begin to experience distortion. If this becomes significant then you may experience something that seems like a change in gain but it is by no means the same thing.
