If government exempted from taxes or reduced VAT off bicycles and cycling-related items, many would be inclined to take on cycling. Even more, wouldn't be so difficult to reduce a percentage of the yearly income-tax return with proof of bike purchase. Badges extended by qualified bike shops (new bike-related businesses and industries would crop up) for every maintenance job would be proof of use of bike and would make you elligible for more tax discounts. The car lobbies could also be encouraged to back up the issue with bike & car combinations, like bikes (foldable?) that could be stuck in streamlined bike-trunks/boots. Even more: corporations would have shape-recognition systems that would certify that you entered their premises by bike and this would have some kinda reward... yeah, I've drifted a bit dreamy here, but still... savings from less road maintenance and fuel demand, along with less pollution and less heart-related diseases in the population would largely pay back to the state if they tackled the thing. There is no shortage of ideas out there.

All that, topped with consistent, repetitive adverts-campaigns, promoting bike usage, along with movie stars with beaming grins advocating for bicycle commutes and you'd see crowds heading to their work places. Looks so simple and easy to me...

(comment from a month ago)

In the winter, I ride by people bundled up and shivering as they scrape ice from their windows, heater running full-blast, and the car is just getting warmed up when they arrive at work 20 minutes later. I'm warmed up within a few minutes of hopping on my bike, and when I get to work I'm sweating and need a cool down.

RFM

Your first sentence states that you only use your car to travel to work and back. Last sentence mentions work AND errands. Which is it?
If you are using your car for errrands now, your mileage calculation (180/month) is inaccurate. One of my occasional errands is 180 miles RT. An "erand" like that makes quite a difference.