The "bag" I use on my stroller is actually a tube with elastic ends. The handles and one set of wheels stick out of it, so it is pretty easily identified as a stroller. When I put it on, I first wrap my empty carseat satchel around the body of the stroller to pad it; thus killing two birds with one stone. The folded bag cushions the stroller, and I don't have to find a place in my carry-on to cram the thing.
I'm weird, I know, but I've actually talked to baggage handlers about the way they handle strollers

I wanted to know what they thought so that I could make it less likely that mine would get damaged in transit or lost. One thing they said was that things mostly get broken during folding, or worse, if they accidentally come unfolded when being moved. They emphasized strongly that when they pick the stroller up, they want it already folded, with the brake set so that it cannot roll when folded, and best of all, secured so that it cannot accidentally unfold when handled. If they accidentally hit the latch and unfold it when they lift it, they will just try to cram it flat as quickly as they can, they don't have time or patience to figure out the proper way to fold it. I asked about bags, too, and they said that if they cannot see wheels, they will usually put it on the baggage wagons unless it is somehow really clearly marked that it is a stroller; they don't take time to read the details of the gate-check tag. (Remember that if the overhead bins on a plane are full, or a bag is too large, FA's will send luggage down to the hold via gate-check. When they come off, those bags normally go to baggage claim.) BTW; credit goes to the friendly baggage guys from SWA and Continental for this info.
I think that if I chose to use a full bag to encase my stroller for gate-check, I'd stencil "BABY BUGGY -- RETURN TO GATE ONLY" in big colorful letters on the outside of it; it might look a little funny, but I think it would be less likely to go to baggage claim that way.