Thank you very much for your question. It is our pleasure to answer it.

In the name of Allah, We praise Him, seek His help and ask for His forgiveness. Whoever Allah guides none can misguide, and whoever He allows to fall astray, none can guide them aright.

Dear sister, the intention is essential for all acts of worship; no act of worship – including wudu – is valid without the intention. Scholars are in consensus that the intention can, but must not be uttered, as it is made in the heart. You should not say, "I intend to perfrom such and such" before any act of worship this to be in your heart not to utter it. You intend in your hear that your are going to pray for example Fajr, just say Allahuakabar" and pray. 

Some like the shafi'i's even say saying it aloud (hearable) is not allowed. Hence, if the place where you do wudu is inside the bathroom – which is the place for relieving oneself and is not used for washing only – then it is disliked to utter the name of Allah in this place, even though it is prescribed to just say Bismillah (when doing wudu). Some of the scholars say that a person should say Bismillah in his heart without uttering it on his tongue. 

And Allah knows best.