Should partition wall between bathroom and bedroom have insulation?

This depends a lot on what the home owner is looking for and their usage. If the bathroom is never ventilated, then insulating the internal walls might not be a good idea as it could lead to condensation against that wall. However if it is well ventilated then it would be a good idea as it would act as sound proofing as well, (not that much if traditional loft insulation is used). Personally I would use it as all of my house included bathroom is well ventilated at all times

I don't follow the suggestion from Thermal Homes Ltd, in essence internal walls don't need to be insulated except where they separate different flats in the same building. It is however good practice to fill all walls with mineral wool as it assists the thermal performance of every room. The bathroom should most certainly be getting ventilated with an extract fan providing an extraction rate of 15l/second. Also the extract fan needs to be of the right specification relating to what zone its being located, Zone 0 being in immediate proximity to the bath or shower, in this instance the fan should be IPX7 rated. Best Wishes Lee Davidson RIBA