Leviton GFCIs constantly trip on shaded pole motors
Anytime you plug in any appliance and it trips a GFCI the odds are that the appliance is not working properly. The easy test is to find another GFCI in somewhere like the kitchen and plug in your unit and see if it trips the device. I really can't speculate why the waterpik is tripping the device but you might see if any moisture is getting into the electrical area of the device and open it up and try to dry it out. Otherwise I recommend that you just replace it or return it under warranty. 

Good luck