I was given one of those brown Seagull gig bags that is structurally sound, but kinda dirty. I was thinking about running it thru a wash cycle in the laundry, or going to a laundry mat and using one of the big washers.
Is it dirty on the inside, or only the outside? If only the outside, try vacuuming the outside with the brush attachment. I've never had the need to do more than brush off the outside, so I can't speak to washing them. Is there a care label inside, or could you email Seagull and ask about washing them?
As far as I know most gig bags are not water proof, if it's just the outside washing it might allow filth inside the padding or worse. I'd just vacuum it off then see if a damp sponge or towel will clean it up well enough.