I don't do this is often, but I'm basically trying to sway you toward a different direction from the White Nylons, i.e. the aforementioned nylon-
core, silver-plated roundwounds: since you said you'd like a classical guitar sound, you might as well try giant classical guitar strings. They're also relatively cheap.
So, I'll only make a small contribution to the main topic, which was
outer-nyloned strings, since the La Bella Copper White Tapewounds do seem promising too, for your tonal preference, according to the poster above.
However, the set that you linked to is a BEADG set: you'd need either the 750C-CB (light) or the 760C-CB (standard), from which you'd discard the low B. Unless you indeed can find the single high C (which I'm not sure you can; try Elderly.com or FretNation.com), to be added to one of the four-string sets, either the 750C or the 760C.
The above having been said, I'll now go ahead with my own
inner-nylon aside, and let everyone else ignore me and carry on as they/you were.
Re the La Bella BG10 set, there is unfortunately a glitch in terminology: in classical guitar Niibori orchestra parlance, a "bass guitar" is actually a baritone-tuned one (B-b). What you need is a "
contrabass guitar" set (with a low B) - either a 4-string, to which you'd add a single classical guitar string (of appropriate gauge) as your high C.
(Again, I'm assuming your bass has a piezo pickup.)
What's the scale length then? So that I can suggest the right set.