Uwe, in the Bert Kaempfert video, 2:23-2:31, you can see two bass players, one playing fingerstyle, the other (Fender J) with a pick.
Yes, I know, earlier than that the bass parts were doubled on guitar with a pic. Later on there was a double bassist and an electric bassist (with a pick), but their parts weren't doubled anymore, the double bassist playing the more orchestral parts. The late Ladi Geisler was the bassist that came up with that sound initially in Kaempfert's big band, he was also Germany's first EB-1 player (later on sodomized with a P split coil!).
And in the vid I posted there is even two double bassists, plus one (what even looks like an acoustic) bass guitarist as spotted by Ilan
and the guy with the J providing the click or - in German - Knack.
I think pick and flats is a lovely combination. A sharp attack with quick decay, it really brings the bass up in the mix without stepping on anyone's sonic toes. It's a bit like slapping for its percussive effect, but there is more tone to the note. Unrestrained slapping is too percussive and not enough tone for me.
