Perhaps Rotosound RB Roto Bass nickel rounds are the same series as or based on the original Swing Bass strings, I don't know.
The wording in the following quote — from an October 2011 Music Trades Magazine article about Rotosound — is a little ambiguous, but would seem to imply James How's Swing Bass roundwound bass strings have been stainless steel since day one:
Although Rotosound was making bass guitar strings as early as the 1950s (...) 1962 brought the earliest version of its signature Swing Bass string, the first round-wound stainless steel bass string, which jolted the market with a clarity and brightness never before heard from the bass guitar.
^ (Emphasis mine.)
https://www.omgmusic.com/pdfs/MTRotosoundOct11Special.pdf
The well-known recounts on the beginning of the Roto-Entwistle connection only mention tweaks to core diameter. Corresponding tweaks to wrap wire diameter are implied, but changes to its composition would certainly have been worth mentioning, and never were: in other words, neither the Hows nor the Who bassist ever said using steel was the latter's idea, and, while it being so would be weird in the first place, it would be nearly as weird if the fact went unmentioned.
Sure, the fact that 1962 "brought the earliest version" does not exclude that there were intervening ones between '62 and '66: was stainless steel introduced at a certain point as a replacement for something else?
Sure, it is once again an argument in absentia, but, it would be somewhat odd that no source mention it.
Either way, in that case said material could have been Monel — the same article mentions 1962 also being the date of introduction of Jazz Bass Monel flats (and leaves unclear just what, and wound in what, How produced for bass guitar between '58 and '62) — or pure nickel but, according to a vaguely-sourced but persistent opinion on the net,
not nickel-plated steel (which the current RB Roto Bass strings are). NPS* in electric guitar and bass string manufacturing was reportedly a very late 1960s innovation:
Pure Nickel Strings
^ This other article is not without its problems: it identifies Pyramid as the 'inventors' of pure nickelwound guitar strings in 1954, and says pure nickels took some time to arrive to North American shores.
Yet Fender's Pure Nickel line appears in catalogues no later than 1955:
Dropbox - 1955 Fender Catalog.pdf - Simplify your life
(The mystery of Fender's No. 90 bass string set is best left to another time.)
* (By the way, according to Roto it would actually be
nickel-plated *iron* at one point.)
Apologies for the inordinate amount of speculation: the above are the only relevant sources I could find.
As I pointed out amidst my contributions to an a propos thread,
[0]=253901&c[thread]=1479245']https://www.talkbass.com/search/37130852/?q=**&t=post&o=date&c[user][0]=253901&c[thread]=1479245
strings is definitely the one very important, yet little investigated aspect in vintage tone fiend research, all but eclypsed by Bakelite bridge saddles, tonewood, scatterwound pickups, coiled cables, valves, drivers and whatnot.