The thing about "white slavery" is that it loomed very large in the early twentieth century western imagination as the expression of racial anxiety rather than a real threat women faced. (There's actually a much broader history of the trope, from fears of white women being captured by Native American groups in the seventeenth century to modern email forwards and viral Tumblr/Facebook posts about schemes to lure them away from their cars or homes late at night, but the early twentieth century is when you really see it as a full-blown public phenomenon.) The term had been used from the mid-nineteenth century to describe class-based exploitation, which could include forced prostitution, but by the 1880s-1890s it became synonymous with the latter as reformers on both sides of the Atlantic used it as an angle to attack low ages of consent and the broader topic of sex work.

This anxiety manifested in both salacious or didactic fiction, and real people's real worries, with a lot of crossover. The common threads in the published fiction involving white slavery were naïve/frivolous young, white, English or Anglo-American women persuaded by men (often immigrants) to make themselves vulnerable in some way, leading to their being forced into a brothel and held their against their will. This reflects on a whole bunch of interrelated social anxieties - young women leaving the protection of their fathers, parents not sufficiently watching over their children, poor feminine judgement, the vices of urban life, immigrants insidiously destroying the fabric of upright WASPdom, and of course unrestrained sexuality. Reports and other non-fiction texts gave estimates in the thousands or tens of thousands to represent the scale of this menace, depending on their definition of the term - to some, "white slavery" was specifically women kidnapped and forced into vice; to others, it was women who entered sex work and then were not allowed to leave it; to still others, it was the selling of sex, period. My previous answer on ice cream parlors discusses the lack of nuance often applied to women's consent and agency in these situations, as well as the fact that we can't simply assume it was all moral panic hysteria.

A great example of this is From Dance Hall to White Slavery: The World's Greatest Tragedy (1912). The first half focuses on the evils of dance halls, where young women are seduced by calculating men; the second on the wiles of white slavers, and the 5,000 young women the authors claim are trapped by them every year. Where the stories in the first half are fairly sentimental moral tales, those in the latter half are sensational, centering on either drugging and rape or deception, and involving the girls being locked somewhere and prevented from leaving until such time as they accept that they have no future in respectable society.

While the more realistic aspects of this anxiety focused on women forced into sex work locally, really lurid fiction-writers would focus on the Ottoman slave trade, which was only officially shut down in the late nineteenth century and could persist in pockets into the twentieth. There was a long-standing fascination with the fact that women from the Caucasus were considered especially beautiful in the Middle East - white women - and there is a great deal of orientalist art depicting nude white women being inspected or presented in slave markets. The "and taken abroad to be slaves to men of color!" twist to the white slavery narrative played on that, and on actual white European women who had been enslaved by pirates and sold in the Ottoman Empire in the eighteenth and early nineteenth centuries. However, by the 1920s this was simply not a thing that really happened, which is why Agatha Christie textually rolls her eyes at it.