I think that's a great idea. When my kids are a little older, I plan to pay them $0.10 or $0.25 a mile for every mile they ride their bikes and I don't have to chauffeur them around.
It's been debated to death here, but the real savings pile up when you can eliminate a car altogether. The lion's share of the expense of operating a car is fixed -- costs like insurance, depreciation and registration don't vary appreciably with mileage.
Of course, cycling is its own reward. The financial benefits are icing on the cake!