What kind of material is on the outside of the bear? If its really fuzzy, I don't think stenciling would turn out so great. If it is smooth fabric, then get some fabric paint to dab on using the stencil.
You can typically mix acrylic paint with fabric medium to paint. This technique may or may not work with your stencil (maybe thin out the paint a bit for the stencil?)
I would sketch the stencil design on the fabric and fill it in with permanent markers like Sharpies.
Annie Sloan chalk paint is fabric friendly, and will paint on soft, however if the bear is furry, you may want to have it embroidered on instead of stenciling with paint.
Paint pens would give you some control.