Just an idea...any men/boys in your home using that toilet...and perhaps their 'aim' isn't the greatest?
If there is any urine smell on the rug, it could be that kitty is trying to bury that smell OR that since he smells it from the people, he figures that is what you are supposed
to do on the rug?
He could also just like to pee on soft things. For your bedding, I would recommend cleaning it (and bath rugs) with an enzymatic cleaner. When he peed on the bed, were the covers rumpled or smoothed? I ask, only because I think rumpled may be more enticing for him to pee on than a smoothed flat surface.
I have two bath-rug pee-ers, both male. No medical problems, but if we leave the bathroom door open and unattended we can be assured of finding a wet spot. Usually it is near where the feet step out of the shower and/or in front of the toilet bowl. My solution was to keep the door closed at all times, hang the bath rugs over the tub to dry after showers and wash the bath rugs more often, as I wonder if the pee-cats were peeing there (step out from shower) because it was getting mildew-y from the wet feet out of the stall.
*I start to dry off IN the shower stall and flip my towel end out to the floor and step on that before stepping bare-footed on the rugs to dry my legs. Husband, on the other hand, steps out immediately (all wet and drippy) onto the bathmat and then begins to dry off with the towel, starting at his head and finishing with his feet, allowing all manner of water to run down his body to soak into the bathmat before he gets dried.
Hmm. Looks like Husband is my problem.
Anyhow, you may find that neutering may have changed this behavior so it has not become permanant. Best of luck and let us know how he does...