I disagree with you on justifying the public expense. Bike lanes increase safety, both for cyclists and pedestrians. One preventable death is worth many millions of dollars. Bike lanes are incredibly cheap when all externalities are factored in.

EDIT: Also, we spend far, far more money on our road infrastructure than on all public transit combined. You are looking at the cost of public transit but assuming that roads were/are free. They are not. Taking steps towards equalizing funding levels between the two would go a great ways towards making public transit better while remaining revenue neutral.