Buses don't have to be faster. They need to be as good or better for the trips you take. If it is 15 minutes to drive to work and 25 minutes by bus that is good enough. If you can get all your other errands done on the bus then you can save a ton of money by selling a car. Note that I said sell a single car - nearly everybody in Dallas lives in a "family" situation with more than one car, so you still have a car for the exceptions while saving a ton of money (this only works if everybody is using the bus for almost everything and so there isn't a conflict when one person needs the car for something weird)!

Also we should not assume only the bus. A train is a useful part of any large transport network. There should be a train between Dallas and Fort Worth that makes the trip in 10 minutes - you can't do that in a car (a race car with a professional driver could beat that if we block all traffic, but no normal car or driver can even if traffic is blocked). Sure the current train takes an hour, but we can make is faster with existing technology.