This is something I noticed when I played guitar more than bass. Before starting to play guitar more seriously, I'd predominantly used Stainless Roto's on bass (they were generally the cheapest back in the day, as well as using a plectrum). When I played guitar, it was with nickel wound strings, and obviously a pick, never had an issue.
Moved back to mainly playing bass with my fingers instead of a plec, and started using nickel wound strings, and really noticed that the skin on my right fingers went really sensitive, and the skin would go white. I'd read in a few places about metal allergy when playing, so bought some stainless strings to try. Problem solved.
I think it's probably more to do with the fact that bass strings are thicker (and having more windings), and are all wound, where a guitar, only 3 strings are wound. But that's not scientific, that's just me.