If the place where you do wudu is inside the bathroom, then it is makruh to utter the name of Allah in this place, even though it is prescribed to say Bismillah when doing wudu. Some scholars say you can say Bismillah in your heart without uttering it.

The reason why it is recommended to seek refuge with Allah when entering the toilet is to seek protection with Him from the devils that frequent places where there are impurities and where ‘awrahs are uncovered.