A bus will normally be considerably faster if your destination is the Magic Kingdom.
The waiting time at Caribbean Beach for a Magic Kingdom bus will normally be between zero and 20 minutes. It's a matter of luck, depending on when you and a bus arrive at the bus stop closest to your room. Actually, during times when demand is high, Magic Kingdom buses typically run more frequently than every 20 minutes. After making its loop through Caribbean Beach, your bus will travel nonstop to the bus station right by the Magic Kingdom gate.
With a car, you'll have to drive to the Magic Kingdom toll plaza and park where you're told to park in the huge Magic Kingdom parking lot (which is a considerable distance from the Magic Kingdom). Normally, you would then walk to a tram stop, wait for a tram to arrive, wait for the tram to fill up, take the tram to the TTC, walk to the ferry dock or monorail station, wait for a ferry or monorail, and take it to the Magic Kingdom gate.
Using a bus, you have the uncertainty and lack of control that comes from waiting for one WDW conveyance (the bus). Using a car, you have the uncertainty and lack of control that comes from waiting for two WDW conveyances (the tram and the ferry/monorail).
I'm not saying that driving will never be faster. If everything goes perfectly when driving, including being allowed to park relatively close to the TTC (eliminating the need for a tram) and not having to wait long for a ferry or monorail, driving could be a little faster. But I wouldn't count on it.