Well, you're dealing with a government agency, so anything not in their personal experience or covered by "the book" will be a tough sell. That being said, however, I would think that if you can provide evidence that the bike is your primary/only means of transportation, you'd have a case. If you live on/near a bus route, that may be tough as they would probably consider that before the bike.
I used to work for a company that was enrolled in a program to encourage commuting. If I biked 4 days a week, I got $40/month in commuter bucks. I could only use them at specific places, but one of those places was REI. I got most of my gear from REI while I was enrolled in that program. Maybe they can do something like that. Their biggest issue is likely to be giving you a direct check, since they can't insure that you'll spend it on transportation needs.