I imagine this is show-biz slang, borrowing the name of the familiar domestic article and humorously parsing it in the sense of “blue” jokes. Many well remember that some of the smart ditties that our Marie warbled ere more or less tinged with squeezes from what the dear girl herself called " the blue bag."

Sting of Bees.—Although the poison a bee emits when it inserts its sting, is proved to be a highly concentrated acid, the application of all alkalies will not neutralize the acid. The more gentle alkalies—chalk, or the "blue bag," are much more likely to effect a cure, and cannot injure[.]Conventional washing powders and fabric conditioners contain chemicals of the stilbene group ‘optical brighteners’ – to whiten whites. These chemicals change light from the invisible ultraviolet and violet spectrum and re-emits it in the blue range of the visible spectrum by fluorescent emission. The blue light coming from the whites balances the yellowy-grey colour of the fabric and it looks white. I searched a number of slang dictionaries and didn't find any slang use of "blue bag," aside from Eric Partridge's note in A Dictionary of Slang and Unconventional English, fifth edition (1961) that Sidneyites had, since circa 1910, used "the Blue Bags" as a slang term for "Newtown footballers." City of Moorabbin Historical Society (Operating the Box Cottage Museum) Book, Carroll, Brian, Early Melbourne sketchbook, 1977 Maugham was a very successful playwright and very familiar with the theatre; and “blue bag” was certainly used in this sense among theatre people during WW II, not that long after Cakes and Ale was published. Here’s actress Naomi Jacob (b. 1884, so about ten years younger than Maugham) writing about her work with E.N.S.A. productions for the troops:

Seeker" wants a remedy for bung eyes. I have tried different remedies, but the best is the blue bag (washing blue) as soon as the eye is stung. Wet the blue bag and apply to where the eye is stung. I don't think it hurts the eyesight. I have three children, and if a fly stings them, they come in at once for the blue bag. It stops the swelling at once, and it seems to take all the pain away.

Why use Traditional Indigo as Laundry Bluing

The little blue bag was stirred around in the final rinse water on washday. It disguised any hint of yellow and helped the household linen look whiter than white. The main ingredients were synthetic ultramarine and baking soda, and the original "squares" weighed an ounce and cost 1 penny. E.N.S.A. shows are blue!” So are many of the shows given in music-halls in England. No E.N.S.A. show is blue at its final rehearsal at Drury Lane, that I can swear. Each show is vetted and vetted most carefully. Manuscripts have to be submitted, and the blue pencil is not spared when objectionable matter is found. If, after the show has gone out, either at home or overseas, the “blue bag” is used too freely that is the fault of the party manager, or going further, the fault of any E.N.S.A. officer who sees the show and hears “smut” and does not prohibit it. Dirt is not wished for, it is not permitted and if everyone concerned did their duty as they should do it it would all be eliminated. Remember there will always be “comics” who like to push in a dirty gag and get a cheap laugh . . . Bluing is usually sold in liquid form, but it may also be a solid. Solid bluing is sometimes used by hoodoo doctors to provide the blue color needed for " mojo hands" without having to use the toxic compound copper(II) sulfate. Bluing was also used by some Native American tribes to mark their arrows showing tribe ownership. [ citation needed] See also [ edit ] Bluing, laundry blue, dolly blue or washing blue is a household product used to improve the appearance of textiles, especially white fabrics. Used during laundering, it adds a trace of blue dye (often synthetic ultramarine, sometimes Prussian blue) to the fabric.