A GK MB 112 or a tc electronic BG250 would be good fits. I have both and have used both in exactly the same manner as you describe. The advertised prices are $375 and $399 respectively but you should be able to get either of them new for less than $350 using a 10% or 15% promo discount through an online retailer. I did.
CV Jazz Bass/Wilde J45s, Matt Freeman PBass/Wilde P46, GK MB112 combo, tc electronic BG250 Combo.