very low power h bridge
MOSFET transistors do not need a current to stay "ON" so potentially they can be lower power. Although you could build your own H-bridge using 2 NMOS and 2 PMOS transistors, I would not recommend that since there are ICs that will be easier to use and have everything you need included.

I found an example of such an IC, the L9110 of course there are more but this a cheap one I could find easily. You can buy ready-made modules using this IC on ebay.