Detailed info on strings in the Fifties and early Sixties is hard to come by. Black Diamond made roundwounds for Danelectro, also available as replacement sets in some areas of the country, as recalled by
@GretschWretch and @TomB (to whom I defer regarding whether they also existed in long-scale version, or only short).
Plus, there is some discussion about (one of?) the earliest, and continuously-available throughout the following decade, Fender-brand sets (pt. no. 90) being actually groundwounds, not true flats:
=16']Search Results for Query: terry foster | TalkBass.com
The above having being said, I don't buy the claim about Jamerson using rounds either, and definitely doubt it being the case during the Detroit era.