Buy a Leduc or an MTD : you'll hear the fundamental of each and every note. LeFay, Aries, Capelli, F-Bass and some others are very good too, but not to the point of hearing the fundamental of your low B.
The type and gauge of string helps a bit, but if your bass has a dire low B unplugged, don't expect much when plugged. An electric bass is before all an acoustic instrument, so when it comes to acoustics, better listen to what a luthier has to say, and certainly not a manufacturer.
But, you can check everything that has been mentioned before, it will improve a tiny bit your low B as well as other strings.
Sometimes, you can get lucky and have a real good low B on a cheap Chinese bass, sometimes.