See, this is where I have to disagree - I think people who insist on driving their own cars should fund those who take public transport.
The government is trying to encourage public transportation - that puts less stress on roads and infrastructure, it causes less pollution and damage to the environment, and means roads are less congested.
Also, public transport is one of those funny things that actually gets better the more people use it.
Fares will go down, and you'd get more frequent services.
It's called negative externalities - the free-market unfortunately doesn't account for all costs.
If I smoke a cigarette - I only pay for the cigarette - but it's those around me that also get sick from the second-hand smoke. That's why the government taxes them.
Likewise, if I buy a gas-guzzling SUV, which churns out black smoke to all my neighbours around - I only pay for the gas - but it's those around me that also suffer.
Basically, if we apply your logic, then we would live in a every-man-for-himself society, where we'd do whatever we could to get ahead, and not care about the impact on those around us.
Paying for what you use and a little extra to offset the negatives is still just paying for what you use.
Further, who pays for the roads the public transportation uses? I have a guess: drivers.
I think people should pay for whatever they want to use.