If you do a standard 9volt rechargable they won't last as long as a normal 9volt. Note the "mAh" rating.
9volts don't stay at 9volts very long once you start useing them. So a battery at 9volts is not going to have an effect because the current draw (mA) is low. You won't start noticeing a low battery untill 6-7volts depending on the preamp and how you are useing it. For example, haveing the bass and treble knobs maxed out is going to run the batteries down faster than having them flat.
You're worring about saving money but you're not going to be changing batteries all the time in a bass AS LONG AS you keep it unplugged when not actually playing it. If you leave it plugged in all the time, you're going to go through batteries.
If you MUST use rechargable batteries use a Lithium Polymer rechargeable. These haven't made into the general market yet but TV and Touring pros use them all the time in wireless mics because the "mAh" is equal to or better than a normal battery. Now that most wireless's have been switching to "AA" these are less in demand.
Untill I got a new wireless I used these and they work great, but are expensive. $20 each plus the charger, but they have a nice long life as long as you follow the directions. http://www.batteryjunction.com/ipowerus-9v-520.html
My basses have always used over the counter 9volts.