We've had a bidet on Joanie M since it was new, 12 years ago. No problem. It has a Johnson diaphragm type pump and just discharges into the cut like the shower does with a switch on tje wall in front of you. We picked the smallest one we could find, made by Ideal Standard.
When we specced the boat I did find another narrowboat, The Antidote, with a bidet but the current owner removed it for extra space.