Is there a way to make activity wristbands read bike rides more accurately?
A decent amount of bike computers have bluetooth or ANT+ on them, which you can connect to your phone or whatever and read out (as a work around). Apps like runkeeper can also track distance based on GPS roughly. 

To quote the fitbit people: 

"All Fitbit trackers are optimized for walking, running, and general household and lifestyle activities. 

It will not be as accurate for activities like biking, but will record steps if you wear your tracker.

For increased accuracy, go to http://www.fitbit.com/activities or click the "log activity" icon from your dashboard to manually log activities like cycling. This will allow for a more accurate estimated calorie burn to be included in your daily totals. Our online database of workouts makes it easy to save and access your favorite activities. For detailed information see How do I log or record an activity?"

Wearing on ankle may work better, but you'd need to check against a cycling computer or something to see how it works. Alternatively, just use something else like Runkeeper or a bluetooth/ant+ cycling computer or enter stuff from your cycling computer in manually after a ride.