I don't know of any software made specifically for that purpose. But do you have a spreadsheet program readily available in the Pilot? My Tungsten T3 (OS 5.2 or something) came bundled with Documents To Go. I would just enter mileage with dates and whatever else classifier info you want in there, then hotsync it to PC for backup/further analysis and reports. Or, depending on your specific needs and using a little imagination, you could probably tweak the Palm OS expense tracker to do the trick.
If you don't want to manually input the mileage but are looking for something more sophisticated (more like replacing your bike comp with Palm), I know it's been done but I don't have any details. But I believe I saw a reference to it here in Bike Forums. Search "palm pilot" here, that might give you pointers.
--J