There are several things you can do to prevent Bonza National Geographic from draining your battery unnecessarily.
To begin with, try dimming your screen brightness, or turning off Sounds from the Bonza National Geographic settings page (click on the cog on the title screen).
Deactivating the video ads which load up on your phone can also help in reducing the battery/memory that your device uses. This can be done by the Bonza settings page as well - simply un-check the video ads option.
If you are still having issues, try enabling ‘Airplane mode’ - just be aware that this will turn off all 3G/4G, texts and phonecalls, and remember to disable it when you finish playing.
By force closing the application after you've finished playing so it is not running in the background on the device is also recommended if having issues with battery use.