From experience, $1 is not enough to keep out the people who spend the whole trip talking about where they want to go to jail for the winter.
And $1 is already expensive enough that if the destination is within 5-10 miles, driving is cheaper if you already have a car and parking, so you are keeping that class of people out.
Though really I find the main reason people don't take the bus is that there aren't enough buses (in time or space) for where/when people really want to go. This is an `m×n` problem.
How are you calculating driving any distance as being cheaper than $1? Surely if you factor in wear-and-tear on the car, you couldn't even get out of the driveway without eating that $1.
Let's say a gallon of gas costs $4 and your car gets 40 MPG. So $1 gets you 10 miles if you only consider gas (which very many people do, even if you think they shouldn't - much maintenance is imagined as time-based, and this is not entirely wrong - cars do decay even if you don't drive them, and insurance only rarely considers your odometer and only coarsely if so).
Wear and tear is generally assumed to be roughly equal to gas costs on well-maintained roads, depending on a lot of varying assumptions of what to include. So, 5 miles.
Adding depreciation, recurring costs such as insurance, parking, perhaps even opportunity cost from capital allocated in a depreciating asset. It starts to not look that cheap.
It really doesn't, though, especially if you've already decide to drive 10 or 20 miles for some other reason. Marginally, the cost of driving 5 miles is quite a bit less than $1.
Upto 0.7 per mile I think? That includes an allowance for depreciation so it's not really a true marginal cost, however for a moment let's assume it is. If the bus was $3 do you think it's wise that it's cheaper to drive a 4 mile journey than take a bus?
And $1 is already expensive enough that if the destination is within 5-10 miles, driving is cheaper if you already have a car and parking, so you are keeping that class of people out.
Though really I find the main reason people don't take the bus is that there aren't enough buses (in time or space) for where/when people really want to go. This is an `m×n` problem.