Dear Polish_Hammer:
Bottom line: There is no USBC rule to prevent bowling two leagues simultaneously, and of course, if the leagues are non-sanctioned, it wouldn't matter, even if there was such a rule.
An exception would be if either league were to have a specific rule preventing such multiple-league bowling -- but it's safe to say that very few, if any, leagues have that provision in its rules.
I once had a teammate who filled in as a sub in a league to our right (while bowling with us), but the lanes involved were only two pair apart, and it didn't prove to be a problem -- and, yes, he used the same ball in both leagues.