I replaced the bridge on my original 60s Baby Bass with a maple bridge (I have kept the original aluminium bridge safe of course!) and have put a Shadow SH950 twin piezo pickup on. That way I have the option of the classic salsa sound from the diaphragm pickup or a jazzier sound from the piezo (in the latter case, you will need to cut the high mids and treble to take away the piezo nasal sound and string noise but it does work really well after careful EQ'ing and actually sounds quite like a real double bass amplified).
In terms of strings, I have put on Presto Nylon wound ultralight strings (the same product is sold in US under the name Eurosonic Ultralights) as these gut-alike strings make me feel closer to playing a double bass. They also sound great on the Baby Bass, with more warmth to my ears, and they are incredibly easy on the hands.
In terms of amp, I can plug straight into my MarkBass Mini CMD121P combo (which has plenty of EQ options). I have also just purchased the new Headway EDB2 preamp and it sounds excellent through that. I will be gigging this tomorrow night, using the Headway as a DI into the house PA with no amp (as I have to schlep the Baby Bass into central London via the London Underground; the gig is in Denmark Street, in the West End)