The only biking I've done in the park is on the bike loop road in Yosemite Valley (and the closed-to-auto roads at the far eastern part of the Valley).
I've seen several bikes on the Tioga Road (Highway 120 East). The stretch is OK west of Tioga Pass--it may even be worth breaking up into a few days. East of Tioga Pass is a steep downhill. I've seen bikes on that part, but be careful--it's steep even for cars!
Other less-busy roads are to Hetch Hetchy reservoir (Mather and beyond), very quiet, and to Glacier Point. Mornings are best.
I would stay away from the roads heading into Yosemite Valley, as they tend to be the busiest (Highway 120 West--Big Oak Flat Road, 140, and 41).
Here's some official and semi-official information:
http://www.nps.gov/archive/yose/trip/biking.htm
http://www.yosemitepark.com/Activities_ ... iking.aspx
http://www.yosemite.org/visitor/frequen ... tion.htm#3