A.F.
Hi Amanda! Since the freezer is your other option you could wash the teddy bear in cold water to prevent the colors from bleeding and after it drys put it in the freezer.
Have you ever heard of the Rainbow vaccum system? My mom has one and it is AMAZING for reducing allergens. They are expensive but they last 30-40 years. You can even "vaccum" your pillows and mattresses. It's worth looking into!