Powering Arduino in Car instaation

Bill, Sure would be. Is your bike 6 or 12 volt?

I use an Opus DCA7 150 watt power supply from http://www.opussolutions.com in my car.

I see that they now have a separate 15 watt power supply that will output 5,7.5, 9 or 12 volts at 3 amps for USD $34 plus $5.00 for one in a case. It works from 6.5V to 30V input.
http://www.opussolutions.com/index.php?p=product&id=24

Might be a couple of dollars but you would only do it once! I will vouch for their support it is first rate, they even telephoned me from the US for installation support (I am in Australia!)

Other than that, be guided by what Ran said in the third post and maybe add an LM808/809 regulator as he said later.