Wires will not change your situation in my opinion. As agedhorse suggested this is an electromagnetic interference/compatibility (EMI or EMC) issue. There are some techniques that can be applied to the bass itself (shielding and grounding) and even the pick-ups (like adding a dummy coil wired with reverse polarity) that might make improvements to some frequencies and sources. However, if just changing position does the trick, you have both diagnosed your problem with a high degree of confidence and developed an effective mitigating strategy.
EMI has a way of finding its way into even the best protected equipment/components and IME a bass guitar with exposed magnetic pick-ups is about as far from that definition as one can get. If positioning yourself to play in a way that doesn't involve only standing in only one spot all the time or contortions that resemble circus acrobatics solves the problem, you might have the best solution. Even additional shielding in the bass control cavity or better grounding of the bass components might not do much more than lighten your wallet.
Many of us have the same issues and we simply stand where the hum goes away. Almost any amp, power supply or even a cell phone held in the right (wrong) way can transmit EMI into most instruments.