In theory you can pull it off (buisness plan, etc...) - but in reality, I wouldn't want to screw around with the IRS. Think about home pffice deductions, clothing for work, etc... "Is this only you used for work? Nope - thanks for the penalty & interest, have a nice day.... Next"
Best bet is to check with an accountant as they may actually know a way to pull it off.
Even then, it's not a credit - it would be a deduction and you can't take most deductions unless you itemize, and it generally doesn't make much sense to itemize unless you have a mortgage or other very large deductable expense (greater than the standard deduction).
Something in the tone of Mr. Schwinn's post made me think this didn't apply to him.
I don't know about the US, but in the UK travel expenses can only be claimed against tax if you are travelling to a non-permanent workplace, i.e. if you work in an office and you cycle there every day then you can't claim, but if you were, say, a courier then you could claim the cost of maintaining your bike as allowable travel expenses and you could claim the cost of buying your bike and things like new wheels, tyres, etc. as capital expenses.