"-zamasu" is the stereotypical "uptown" Tokyoite speech (contrast with Shitamachi/Edoben, the downtown working-class equivalent). It functions as a copula (like all the desu/da variants), and is basically derived from "gozaimasu".
"-zamasu" is stereotypically associated with rich wives who live in the "Yamanote" districts of Tokyo. Suneo's mom from Doraemon peppers her speech gratuitously with it. Helicopter moms also sometimes get this accent, and there is some overlap (between rich wives and helicopter moms).
The "rich schoolgirl" archetype also typically speaks a formal, polite acrolect (AKA ojousama speech) that is also derived from the Yamanote dialect (Meiji-era schools around Tokyo, principally). There is some overlap with normal "feminine speech" (onna kotoba), but the ojousama archetype tends to use more formal and polite syntax on a more frequent basis.
In written fiction most of the ojousama 'dialect' speakers use similar syntax and vocabulary. There are further differences in spoken form though, mostly with how certain consonants/vowels are pronounced and how the pitch stress are intoned. In particular, Kanzaki Sumire and Shirai Kuroko have highly "affected" Yamanote accents, despite not using -zamasu.
McQueen doesn't have quite as strong a accent though. Usually, that is. It's occasionally exaggerated in comedic scenes, especially in imagine spots by other characters.
The English equivalent would be someone speaking in a posh British RP accent, or the American Mid-Atlantic equivalent. Older dubs tend to like giving posh British-sounding accents to such characters.
Additional notes
Note that Standard Japanese is also based (principally) on the Yamanote dialect, though most people wouldn't consider that to be a dialect. Like how RP is also the basis for 'Standard' British English, yet still has its own peculiar quirks to 'Standard' speakers.
Another consideration is that most of the differences between Yamanote and Shitamachi have faded in current times among real-life speakers, especially among the younger generation. Same goes with feminine vs masculine speech, to a lesser extent. In general most of the distinction is preserved (and/or exaggerated) in fiction because it provides a convenient way of distinguishing characters as well as providing a 'shorthand' for certain expected character traits. This is also true for English dialects in real-life when compared to their fictional counterparts.
TL;DR: Golshi is partly ribbing on McQueen's '-desuwa' speech. Other part is her hoping McQueen gets a more exaggerated posh accent for the lulz factor.
