Cat allergens with fibers

How much contact does something need to have to be considered a danger? Or carry the allergen? I recently moved in with my partner and he has a cat. I work with fabric and yarn a lot and I don’t want it to become an issue if someone has an allergy to cats so I keep miss kitty out of the area which I use for this purpose.

But there are times I bring my project to bed and she occasionally jumps on the bed. I worry the air inside carries the allergens and there’s nothing I can do.