Get your wife to agree on the cost savings equation, and then negotiate the value of each term.

The equation goes something like this:

(Savings by bicycle commuting) = (Reduction in gas costs) + (Reduction in auto insurance cost) + ( Reduction in auto maintenance cost) +( Reduction in tolls and parking fees) +(Reduction in auto depreciation) +(Reduction in health care costs) + (Reduction in gym membership fees) + (Reduction in costs for coffee and donuts while driving) + (Renewable energy credits) - (New bike and equipment costs) - (Bike maintenance costs) – (New bike clothes costs) – (Costs for extra food due to increased exercising)