How can I reduce the noise from a bathroom fan?
The first thing to check is if the fan unit is properly and firmly mounted in the ceiling and that the actual motor/fan portion is tightly secured in the housing. If the vibration is being caused because the fan is unbalanced or the bearings are worn, there is probably not much you can do for it. New fan units are not that expensive and are much quieter than older models. Noise ratings are posted on the units and measured in Sones. The lower the number, the quieter the operation of the fan.  Maybe it is time for an upgrade.