Any concept of duality (Life/Death, Male/Female, Light/Darkness etc) is a suitable meaning for the Bident, although the Twin Serpents fit it both in shape and meaning.
I imagine two intertwined serpents with their heads separated, representing the dual aspect of life: if one isn't there, the other one falls. Being held by Hades likely means the cycle of death completing life: both honest and liar, good and evil, young and old will die.
The symbol of Pluto can also be interpretated as Hades holding the Bident (the low cross as I call it, seen in Ceres, Venus, Mercury and any other astrological symbols representing tools held by gods), the Bident itself meaning duality and the circle meaning the third/whole, the union of two aspects in both and none.
This is just my interpretation, though. I might be mistaken or have missed complementary meanings, since this is the first time I interpretate this symbol.