We need some more headlights working in the bottom picture!! If its a cloth bag, I'd separate from the tube and put it in the washing machine on delicate cycle with like colors of course! Shout or Spray n Wash stains.
If its vinyl, I would just soak it in laundry tub. Laundry detergent, some Lysol, whatever. I recently bleached a vinyl Eureka F&G bag. It was primarily white but does have pink and blue stripes and the Black ink F&G label, all of the colors survived well, but the dirt and stains are gone!! Rinse thoroughly then hang dry for a few days, depending on your weather, you could put it out in the warm sun!