Carrying a whole roll of duct tape is awkward. It's bulky and heavy, and you seldom need more than a few feet of it for an emergency repair. So it's common to wrap a few feet of it around some other object, like an old gift card, or a water bottle, or any other object.
Duct tape is sticky enough that if you unwrap it from the roll and wrap it around a gift card, it can still be unwrapped and used to stick something else together. As long as the sticky part doesn't stick to itself, it's re-usable multiple times.
I always pack a small repair kit when I travel, which includes one of these tape cards, plus a few other odds and ends for making emergency repairs to luggage or other items, just enough to get me home where I can either do a permanent repair or replace the damaged item. The tape card is in the upper right corner of the photo; it actually holds a length of duct tape plus a length of vinyl electrical tape. I think that's about six feet/two meters of each tape (it's been a long time since I last wrapped it so I can't remember exactly), which is enough for most small temporary repairs while traveling.
Note: When the previous poster mentioned 'grocery bag', I believe they were referring to the re-usable type of grocery bag available for purchase in most US store, not the flimsy disposable plastic bags that come with most purchases. Obviously, these disposable plastic bags are not large enough to carry a messenger bag, but some of the re-usable bags are.
My travel repair kit
Great option. I have some of that, I may swap out my duct tape for it before my next trip.