Does anyone know of a non-toxic substance I can spray my bed linens with to keep pets off my bed?

I don't know of any spray that would deter them, but I've read that covering the bed in aluminum foil scares dogs when then jump on it, and then they get off. You could try that.

we put a couple of laundry baskets on our couch. the dog avoided the couch after that. the foil idea may work. cats may just burrow under foil. try it. can,t hurt. avoid sprays or chemicals. they only work outside, not in the house.

Try researching smells that they don't like, there could be a herbal or aromatherapy whiff that they run away from