Thanks everyone, it's good to know I am not the only one bathing my baby doll weekly!
He is not really greasy. His fur just gets a little clumped in the face area after a week or so.
And, he's half Yorkie half Shih-Tzu so I am not sure if that makes a difference.
Since it seems lots of babies get bathed once a week I think I will keep it up unless I notice a problem. I just love when he is all nice and fluffy!!!