How did Pharaoh prevent people from seeing him use the Bathroom at the Nile?
We know he went early morning, but what prevented others from seeing him?
A source for this information would be Highly appreciated.
According to the midrash to which you allude (Sh'mos Raba 9:8), Par'o was intentionally hiding from people in order to lead them to the false conclusion that he was a deity. If so, I would assume he looked around to make sure there was nobody there before proceeding. He was looking for them but they were not looking for him. Moshe, on the other hand, had the advantage of having been told by Hashem that he could find Par'o at that place and time and therefore could more easily have snuck up on him.
Da'as Mikra actually goes a different route to explain why Par'o was out there in the morning, namely that he was just on a leisurely royal riverside stroll (in keeping with the Ibn Ezra and others), but emphasizes the ominous sneaking up nonetheless. It says that when Hashem instructed Moshe using the word "הנה יצא המימה" He was pointing to the spot by the river where Moshe should stand, implying that Moshe actually got there earlier in the morning than Par'o in order to stand threateningly with staff outstretched.
I heard a shi'ur that cited the Pa'ne'ach Raza giving three answers to this question: