Andrew and Mags nailed my intentions pretty well on this one. Good discussion thus far, so I'll pat myself on the back and say job done.
It's compelling on a gut level to say that legalizing bikes in Wilderness would start the slippery slope to motorized use, resource extraction, etc, but this is factually and legally incorrect. Motors and non-grandfathered commerical use are specifically prohibited in the original legislation, while mountain biking is not addressed at all, as it did not exist as such. In the late 80s the Forest Service put an administrative rule into effect qualifing bikes as mechanical transport, and thus prohibiting them from Wilderness. Hypothetically it would take nothing but some typing and a signature to reverse that. I think it's pretty non-controversial to admit that the difference between bikes and skis (allowed in Wilderness) is one of degree rather than type.
I'm most sympathetic to the makes-the-place smaller argument against bikes. In many Wilderness areas the distinction is largely academic, but in some it's very relevant. The height of my mountain biking powers 6 years ago coincided with the time I hiked the southern chunk of the JMT, and based on the trail which wasn't covered in snow I reckoned I could ride more than enough to make it a worthwhile bike trip. Given how much slower I would hypothetically be on the climbs I doubted then and doubt now that overall cycling would be much faster than hiking. Maybe 35 mpd on bike versus 30 hiking based on comparable effort.
On the other hand the Bob Marshall and Teton Wildernesses are quite gentle in most places, and once the mud clears up in late June or July would make for some great cycling. It would be quite possible to ride across the Bob the easy way (N Fork Blackfoot to Meadow Creek) in a long day. An aggressive hike and packraft itinerary of the same route is an overnight, if not more.
In summary, I'd be ok with allowing bikes in many parts of the Sierras, but only if the Whitney Portal road, Trails End road, North and South Lakes road, and highway 120 are permanently closed to cars. Nick is right in that a lot of the land worth "saving" in the lower 48 is locked up. Time to start pushing back, shutting down roads, and letting them rot.