I just estimated battery life by taking the given estimate of 500 mAh (milliamp hours) for a new alkaline battery being discharged at a fairly low rate (2.5 mA or 2.24 mA is still a fairly low current flow when considering discharging the battery) and then dividing that life expectancy by the actual current flow (the 2.24 or 2.5 mA). That is what would give 200 hours in your case, or 223 hours in my case of battery life (if you were playing all the time). If you or I played 2 hours per day (and had the bass cable unplugged when not playing), we would expect to have the batteries die in 100 or 111 days.
I'm thinking about wiring in an additional spdt mini toggle onto the control plate to be able to cut the connection between the batteries and the ring on the output jack, so that if you played in passive mode, you wouldn't be draining the battery. If you throw this proposed switch when the bass was switched to the passive mode, I think you wouldn't get the loud pop that would happen if all was wired into 1 switch (that changed mode from passive to active and vice versa, and also turned the current on and off). I'm also waiting to hear back from Sire about this stuff.