Two basic options for converting this to battery power.
The first is LEDs. While you could glue/place/attach individual leds to each bulb, that would be a mess to attempt. A single 1W or higher LED would be plenty bright. You could go with a bare LED star, or use commercial 12V LED modules. You could even use a LED intended for car lighting, in a nice omni-directional shape.
The other option is a CFL bulb. You could hack one, by taking out all of the electronics, and using a disposable camera flash circuit, or bug zapper (Both are low voltage to High Voltage transformers) to drive the bulb from a pair of AA batteries. Or you know, you can just buy a CFL that's designed for 12V DC.