Ok, here's what you need: A paper towel or wrapping paper tube*, the plastic bags you want to have on hand and five minutes. Unless you like the looks of that cardboard tube as is, you'll also want some wrapping paper, tape (or glue) and scissors. (Or, if you have kids, you could skip the wrapping paper and let them decorate the tube(s) with stickers or whatever you have on hand.)
This is a great use for that little piece of wrapping paper that's left on the roll or that annoying uneven piece.
Now for the bags - just fold in (more-or-less) thirds and roll them up. This only takes a matter of seconds, assuming you keep your inner perfectionist in check.
Then stick the bags one by one into the tube.
I put the whole enchilada under the front seat of my car to await the next spill or chocolate meltdown or...other thing that needs bagging. You might want an extra one for your diaper bag or stroller.
Have another idea? Feel free to comment. :)
*I don't recommend using a toilet paper tube because it could be germy. Don't think about that or the toilet-paper-tube crafts you did as a kid for too long. Actually, my Mom's preschool no longer reuses them for that reason. If you want a cardboard tube that size, cut a larger one down.