A high-fiber diet sweeps the G.I. tract of all bile, and there's nothing left to be reabsorbed.
The body then has to make new bile, from cholesterol.
How does fiber lower cholesterol? - Yahoo! Answers
"Dietary fiber is also associated with improvement in diabetes and reduced risk of colon cancer. The most important mechanism is by inhibiting the reabsorption of bile salts from the gastrointestinal tract. The bile salts are synthesized from cholesterol and released into the gastrointestinal tract to help absorb fat soluble foods. Normally the bile acids are reabsorbed at the end of the small intestines (ileum) and recycled again. Inhibiting the reabsorption of bile acids means that more cholesterol will be used to synthesize bile acids."