Hello Andrew
A far as I know, bailey tend to use on board self priming pumps not submersible ones.
The self priming pumps are usually displacement types with reciprocating pistons/diaphragms and valves. These inevitably set up vibrations and because they are carried inside the caravan body and usually fixed to panels, they do tend to be noisier than the external submersible pumps.
You can try decoupling the pump body from the wood work by using soft rubber pads, but they will always produce some noise.