It takes 91% less energy to recycle a plastic bag than a paper one (17 BTUs versus 1,444 BTUs)! Despite this fact, paper bags are recycled at a much higher rate using mostly new tree pulp each time.
It also takes a fraction of the energy to produce plastic bags initially! Plastic bags require a mere 594 BTUs, while paper bags take over four times the energy - 2,511 BTUs! Also, in paper in today's landfills does not degrade substantially faster than plastic does.
If you really want to waste less, get a reusable shopping bag! For more recycling info.