The size of a bull bar is debatable, and I cannot answer it. There are probably things under Construction rather than MOT that apply.
Certainly if your car is fitted with a push operated washer, his is not reason for failure. The regs state ". The windscreen washers do not provide enough liquid to clear the windscreen in conjunction with the wiper(s)" is reason, so if your pump pumps he cannot fail it.
More info is available at ukmot dot com slash manual.
One of my vehicles has a push washer, and vacuum wipers. I will enjoy getting that tested. If you feel agrieved enough, firstly ask him to show you where it says washer pump can't be manual, where it says about screen size, and ask him for the number for the MOT testers inpectorate, so you can check with them.