A search in internet for "dealing with cat fleas naturally" will provide many hits. Good thing is; the cat is not a house pet.

Changing/washing all bed linen and vacuuming bed mattress and whole house should help. You can get a cat flea collar, cut it up into small pieces (wear gloves), and place in vacuum dust collector. It will kill any fleas sucked in there.

Sure they are fleas (have you seen them?) and not bed mites? If allergic to bed mites, bites will react and show .