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.

This Ngram find references "blue bag" multiple times, using it in a way that makes me suspect it's a term for some specific type of luggage. There was a well known intellectual property dispute between two manufactures of this type of product. The legal action arising from this is still cited in English law disputes. (Ironically, the two companies later merged with each other!)

How do you use True Indigo as Laundry Bluing?

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 ] Many washerwomen—charring-women, notably—have an immense fondness for blue, for they can hide for the tome being, by its aid, any carelessness they have been guilty of as regards washing thoroughly. Blue covers up the yellow hue consequent upon this. Very blue clothes, too, look bad, but a slight colouring of it adds to the beauty of well-washed garments. 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: 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.

Laundry bluing is made of a colloid of ferric ferrocyanide (blue iron salt, also referred to as "Prussian blue") in water. But their humour was really of a very quaint and infectious kind, and they were always welcome, especially when they used less of the "Blue Bag."

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. THE USE OF BLUE, AND THE ABUSE. Much blue is very objectionable. Dip the blue-bag into the [clean, cold rinsing] water until it is just perceivable that it has been in. And earlier still, from Albert Chevalier, Before I Forget: The Autobiography of a Chevalier D'industrie (1901):

Storage & organisation Furniture Textiles Kitchenware & tableware Kitchens Lighting Decoration Rugs, mats & flooring Beds & mattresses Baby & children Smart home Bathroom products Laundry & cleaning Plants & plant pots Home electronics Home improvement Outdoor living Food & beverages Christmas Shop Shop by roomThey built up a major international brand, with various lesser rivals, notably Mrs. Stewart's liquid bluing Context suggests that what Maugham means is off-color or bawdy jokes. Note that Mrs. Hudson's use of the blue bag is contrasted with her ‘propriety’: 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 . . .