That's the signature sound of
Pino Palladino playing a fretless. I haven't heard the song recently, but I don't think there was much more than chorus in the actual bass sound. A very good example of the sound coming from the player more so than the gear. There are plenty of keyboard parts in the background, though. It was the '80s after all.
-- T. G. --
[edit] Pino played fretless P-basses, BTW.