I think a lot of the properties of wood relevant to a luthier building acoustic instruments are of little relevance to electric instruments, where pickups and their positioning dominate the sound.
However, with a bass (more so than a 6-string, let alone a mandolin, because of the mass of the strings), the stiffness and density of the wood will have an effect on the absorption of vibration ... potentially changing the characteristics of the attack and more significantly the sustain. Ash is often denser, similar to the fruit woods, than alder, and is stiffer