For cat related asthma are there any treatments beyond bronchodilators or steroids?

Several Options: For allergen induced asthma there are several options: avoidance; use of inhaled steroid and / or bronchodiltaors; other antiinflammatory medications; and allergy vaccine therapy.

Catectomy: Removing the cat from your life works very well, although almost no one is willing to do it.

Cat in or out?: Cat sleeping on your head? Not much chance of improvement - unless you kick the cat out of your room. Cat out? Good. Open the windows or use a hepa air purifier to decrease airborne cat dander. Scrub down the room - bed, floor, walls, ceilings. Allergy immunotherapy takes time - a year or more - but done right it really helps especially if exposure is intermittent. See an allergist for help.