Despite Norma's worry about admitting Norman to the hospital and even though she was clearly surprised at the cost for a month (between $20-40,000 per month), she later tried to sell the benefits to Norman. Money is already tight in the Bates household but she is willing to do anything to help Norman and the emotional need that comes with that outweighs the financial costs. Also, whenever a show introduces a psychiatric hospital as one of its regular haunts, it's never dull. Imagine the things that Norman will get up to in there...