Driving is already more expensive than transit almost anywhere and for almost everyone. Full ownership costs for a car in a developed country tend to be in the range of 50+ c/km (80c+/mi) while bus fares tend to be flat rate of $2-6/trip, by the time you hit a 10km trip it's cheaper to take the bus/train.
People drive because of comfort and convenience, not cost (except those incredibly bad at math, which is a group probably large enough I shouldn't completely discount them)
For transit to win over car drivers they need to improve the convenience and comfort. improving cleanliness and comfort on transit vehicles helps, more express routes help, better schedules help.
Trouble is, those improvements are quite costly to implement. (arguably cleanliness is fairly simple, the rest less so)
People will take transit when it stops close to their origin and destination, has few stops on the way, is not crowded, is clean, and comfortable, and departs when they want to travel. It's a tall order.
Of course some cities have taken the opposite tack, they realize it's hard to make transit better, so they are attempting to make driving worse. This is done by intentionally avoiding needed road upgrades, removing driving lanes, blocking routes, adding transit only lanes or roads (make no mistake, they don't "add" them, they replace an existing road or lane). This does actually work. If driving to downtown takes longer than the train, and you can't find a place to park when you get there, you'll likely take the train instead.