To help tilt things further towards biking, I think you shouldn't be looking at the absolute calories burned when biking, but rather, the calorie differential between biking and whatever other activity the person would be doing, since we burn calories even when sleeping. From the same source, "Police, driving a squad car" burns 141 calories/hour (no mention if that includes donut-eating), so if you ride your bike instead of drive for that half hour, the calorie differential is only 180 calories, not 250 (this is good news for the people trying to save money by biking, but bad news for those trying to lose weight!) That brings the cost of the extra calories down to 27 cents.
Then, removing the "6 miles" from the numbers to simplify it, we arrive at 4.5 cents/mile for cycling fuel, and 17 cents/mile for driving costs.
For a pure fuel-vs.-fuel cost (removing oil change/tire-replacement costs), using MMM's $3.50/gal@35MPG number, we have 4.5 cents/mile for cycling fuel, 10 cents/mile for driving.
To sol's point, even though it's a >2x difference in fuel costs, it's still pretty hard to justify bike riding as a huge money-saver based on fuel-costs alone. If you do that 6-mile (round trip) commute every workday, it saves you only $82.50/year in fuel-cost. I take this more as an indication of how ridiculously, stupidly inexpensive gasoline is (even at its "high" price right now), rather than an indictment of cycling. The fact that a few thousand pounds of steel can be lugged around for only a little over 2x the cost as the incredibly-efficient human+bicycle combination is just crazy. Back when gas was $1.50/gal, it probably *was* cheaper than cycling.
My commute is about 13 miles round-trip, and since I attack it more aggressively (and weigh more) than average, the calorie differential for me when riding my bike is 650, or about $1 in "fuel costs", which equates to 7.7 cents/mile. Just barely beating MMM's 10 cents/mile gasoline cost! "Luckily", my car isn't as efficient as MMM's example, and it takes premium fuel at about $4.50/gal these days. The result is that I pay about 17 cents/mile for gas alone, which restores the ~2x differential for my situation. Yay?
So I can say that I save $1.25 in fuel costs every day that I ride my bike to work rather than driving, which would equate to $300 a year if I rode every day (not gonna happen). Yeah, every dollar makes a difference, but when I'm already saving over $50,000 of my income every year, and my net worth can jump up or down $3000 on a normal day in the stock markets, it's pretty hard to get a strong motivation from that <$300/year. So I think we all agree (including Bakari's commenter) that advocating biking based on $/mile alone is probably not that effective. Luckily there are a ton of other motivations that keep me riding, not least of which is the fact that food, unlike gasoline, tastes awesome when you eat it, so I'm happy to pay a bit for the opportunity to eat more of it without getting fat!