What could cause dishwasher waste water to back up into the bathtub?
Clog or Restricted Drain
The most likely cause of this would be a clog, or restriction in the drain line. When the dishwasher discharges, it's too much water too fast for the drain to handle. The water likely backs up into the tub, because it's the easiest escape for the excess water.
If there is a clog, it would be somewhere in the drain line after the tub (which is why it backs up into the tub). Without actually being at your house, it's nearly impossible for me to be more specific.
I would start with a liquid clog remover (like drain-o, liquid plumber, etc.), which I would pour down the tub drain.  Make sure you select an appropriate product. for example if you have a septic system, choose a product that is safe for septic systems.
If that doesn't work, you could snake the drain (or have a plumber do it).
Full Septic Tank
If you have a septic system, it may be time to have it pumped and inspected.  When septic tanks are full they cannot leech water fast enough, often times the result is waste water backing up into other fixtures.
The only solution here, would be to call in a professional to service the tank.