I don't know about the Classic Vibe P-Bass, but I've played the CV J-Bass, and it's a fine bass. Usually with Squiers it's a good idea to change the electronics to better quality items, like CTS pots and better pickups. I think the SPB-1 or similar quality and a good set of flats should get you that smooth sound you're looking for.
Hofner Group #34, Canadian Club #137, Le Club des Francophones No. 12, Straight-Forward Bassist club #4, Squier Affinity Club #11, 50+ Club #16. Go in, lay it down, and get out.