How big are you thinking?
I've used a Dowco Iron Rider Roll bag on the passenger seat of a few bikes, including my ST1100, that is about 15 L.
I've also used a very large 110 L roll down dry bag. That one had a stiff bottom floor and opened along the long axis. A luggage rack is recommended to help support it since it was over 30 inches long and I would mount it long-ways with the bike rather than across the seat.
I've also used several sizes in between, but almost all of those were dry bags of various sizes.
Can you tell... aside from the Iron Rider bag I prefer dry bags that are inherently rain proof and don't simply have a rain cover to put over them.
I still have the Iron Rider bag but don't use it any more.