Only ever had a SR500 active bass. Seems hard to flatten the battery (but did not leave plugged in on standby). I read a little under 1.5mA using same method, so a lower drain bass. It is pushing it a bit to design electronics to run on 9V, 18 would be better. So rechargeables, NIMH and Lithiums are too low a voltage for a 9V circuit to function as designed.
Incidentally, I bought a "trail camera" a few years ago. It came with some Energiser Ultimate Lithium batteries and these were recommended by the manufacturer, worked better than Duracells which were rubbish. It was the highest spec Energisers. These are not rechargeable so you get the full 9V, higher capacity. might be worth trying but maybe 6mA is a high discharge bass. I have a headless Ibanez, I'll get it out and measure it