People will switch from cars to bikes only when they've exhausted all the cost reduction alternatives.
One way to cut fuel expenses approximately in half is better trip planning and combining trips.
Another way is by using a 40-50 mpg small vehicle.
Another way is by intensive carpooling or vanpooling.
I can't think of much else a person could do to stretch the fuel budget. So the maximum cost reduction that can be done is a factor of 8. If the threshold of pain in the present non-conserving environment is $3 a gallon, as evidenced by the increased discussion about gas prices here, some people will start to feel they have run out of alternatives when the price reaches $3 x 8 = $24 a gallon. Of course, other motorists would have enough income to be able to afford even $24 a gallon.
If even a few percent of motorists try to switch to public transit, the present systems in most U.S. cities would be unable to accommodate the demand. So in an apocalyptic scenario, mass China-style cycling would really be the only alternative.
I doubt gas will come close to $24 a gallon for many years. Long before it reaches that point it will be economically feasible to extract oil from unconventional sources like Canadian tar sands.
So I think we will never see the average motorist on a bike. A more interesting question would be, at what price will we see the number of bike commuters double or triple? We may not be far from that now.