If you don’t want to take your H dust bag, someone somewhere upthread here (I think!) recommended
UNIQLO reusable totes. They’re inexpensive, but really nice; I picked up one in each size after I read that recommendation (U.S. $2.90 each). They don’t zip closed, or have a drawstring closure, but they will protect your bag. They come with a matching fabric ring, for lack of a better description, so you can roll and store them easily when not in use.
I sometimes travel with my H; it depends on the destination. When I travel with my B30, I pack smaller items inside it first (crossbody, clutch, pouches with tech cords/meds/other odds and ends). Those items go in dust bags of their own, or I use soft pouches, so they don’t scratch the inside of my B. The B goes in a dust bag and that goes inside my LV Neverfull GM. There’s still room for larger items that won’t fit in my B, such as magazines and my iPad, as well as items that need to be easily reachable, such as wallet/passport and phone.
OT: I’m super impressed with those of you who can manage carry on luggage only for 14, or more, days. We need a thread dedicated to packing with a carry on so you can share your advice (and photos)! I can manage for some trips, but week-long, colder destinations require heavier clothing, which takes up more room, and cruises require two sets of clothes per day (casual/swim for day, something nicer for night), which means having to pack lots of stuff.