I learnt the Igros Moshe a while ago.It is Igros Moshe EH 1:114,he says that todays bathrooms are a safek bais hakissai and one cannot wash in a bathroom for a meal,one could wash his hands in the bathroom for davening as long as they are dried outside.It is certainly more preferable to wash outside.
Also see Rivevos Ephraim(talmid of Rav Moshe ) 6:3:1.