"The most efficient bike" will have to propel its rider the most distance on the least fuel; so, it must be light AND sturdy. Light, to take less energy to pedal; sturdy, to last long enough to to recoup the initial investment.

Bicycle: $80-15,000.
Food/Fuel: variable, anywhere from $0.15 for a pack of ramen noodles to $1000 for a political fundraiser.
Joy of riding: BEYOND priceless!

So, my answer is, my Jamis Dakar XLT 1.0; 34 lbs., 5.7" suspension travel, 27 speeds, dual discs, and never less than 2.0 wide tires. For over four years, it carried me through joy and pain, sunshine and rain, everywhere I needed and wanted to go. When the frame died, I cried.