Everyone's situation is different. Myself, I have been turned down for *many* jobs because they required a car, even jobs that I was otherwise qualified (or overqualified) for. It's at the point where the main thing I worry about in an interview is whether they'll ask if I have a reliable vehicle. I'm not in a profession where you can telecommute, and although we have decent public transportation in my area, it doesn't go everywhere.
IMO, you can certainly use a bike to commute to any job--but it's not always practically feasible. I think for a lot of people your choices are
a) restrict your job search to a relatively small geographic area
b) accept that it may take you 1-3 hours to get to work (one-way) through a combination of public transit and bike
c) move to an urban area.
But this, of course, depends entirely on where you live and what you do.