A B-string needs some room to vibrate. A thinner string vibrates with more amplitude, as it's less tight. I don't think that's the way to go.
First of all the bass should be set up with the standard amount of neck relief. From that point action and other settings can be optimized. I play a four string BEAD tuned bass which is set up pretty low, but I do have to be carefull not to smash the 0.130 B-string against the fretboard. I guess that's the compromise which you get for free with B-strings.