Consider also how different it is from chases scenes in modern movies. The average shot length for this 9 1/2-minute segment is 3.7 seconds, with many shots lasting four or five times that long. I don't think any car chase in a Hollywood film made in the last 20 years has done that -- quick-cutting is the norm now. And while that frenetic style has its place (I love the car chase in The Bourne Supremacy), it would be hard to argue that Bullitt's chase sequence would have been improved by faster cutting. The long shots let you see where the cars are in relation to each other and to their surroundings. Several shots give you a driver's-eye view of the action, and it's like riding a roller coaster. You couldn't get that effect with a series of split-second shots. (Bullitt won the Oscar for its editing, by the way.)
McQueen did his own driving for all but a few shots. (Legend has it he intentionally leaned toward the open window so that viewers could see it's really him.) It's clear there's no fakery in the high speeds, either: Those cars really are going that fast, and they are just barely avoiding countless wrecks. (Another difference between this and most modern car chases: There's very little collateral damage, up until the end.)
One other thing to notice is the music. Lalo Schifrin's jazzy score is moving along at a steady pace as things pick up: McQueen sees the bad guys, starts following them carefully, nothing too dramatic yet. It's not until the 2:50 mark that the killers peel out and the chase really begins -- and the music stops. There's no more music, and no dialogue, for the rest of the sequence. Who needs music and talking when you've got muscle cars skidding around the streets of San Francisco??