Hmmm, I'd guess at this stage it is probably more bad behavoir. I'd probably get a totally new dog bed (unless you can wash the entire thing so there is NO urine smell left at all). I would then put the new bed down (maybe just try an old comforter in the same spot for now that can be easily washed) and put a litter box right next to the bed. You can then graduate to moving the litter box farther away until it is back to the original spot.
You could also try covering the dog bed with some aluminum foil, most cats hate that