I don't think rechargeables are much competition for alkalines in a bass. The oldest kind - Nickel/Cadmium had a lot of problems with memory effect - you need to charge them fully, then discharge them fully, otherwise they hold less and less charge. That does't work in an instrument at all - if you run til you start hearing distortion, that's the worst case for a Ni-Cad.
The more common type you see today are Nickel-Metal Hydride or NiMH. They have much less memory effect than NiCADs but you still run into the same problem. One of the problems of NiMH is that when the power starts to drop off, it drops off very quickly. Both NiMH and NiCad are not very environmentally friendly at disposal.
The kind of batteries used in cameras and laptops are Lithium Ion. They are very light, hold a lot of power, and can handle very heavy intermittent loads (like a camera flash). They're better environmentally. But the bad part here is that they are very expensive (camera batteries are $40+, laptop batteries $100-200) and require a smart charger to monitor the battery temperature while charging. If you try to charge or discharge the battery too fast, it can get hot or even ignite. When you hear stories of flaming laptops and iPods, these are lithium batteries.
All these other battery chemistries make less voltage as well, so you lose headroom in an audio app like your EQ circuits.
Alkalines are good at the small long-term drain, are cheap and easy to replace. Hard to beat that for a battery that lasts 40-100 hours in normal use.
David Fung