If you're not carting a boatload of luggage, you can probably get there by train for a lot less (but, with luggage, it would cost less only to create more angst).
Yes, it costs about 120 CHF. I would take the train. There is a direct train from the airport to Baden every hour on the :04 and costs full fare CHF 15. Then if you have to you can always take a taxi from the Baden train station to where you need to be.