I think I'll add my 2¢ to this discussion.
Whenever I have family down, staying at a Disney Resort, we always use the provided transportation. I personally have never waited more than 9 minutes 32 seconds for any bus. (And yes, I time it.) We've stayed at the CR, Poly, GF, and Music. As a driver, I get to see what goes on backstage with the dispatching. I can assure you, no one works harder than our Flex & MOD Dispatchers on getting those busses out on time. And 98% of the time, they are right on time.
Most "Extended Waits" are usually not as extended as they seem. Not to say the occasional service issue don't happen, but rather, the vast majority of the time the bus is on time, it just felt like a longer wait than it was. The more anxious one is, the longer it feels like. Also, if there's one person at the stop who makes a comment, it acts like a domino effect. Pretty soon, everyone is making comments... and the supposed wait time increases.
Often times, I'll see a bus exiting a resort just as I'm entering. When I see that, I know the wait has been no more than 10 minutes, but yet I still will get a group saying they haven't seen a bus in 30 minutes. Happens all the time.
Getting back to the topic at hand, though...
You will not neccessarily save time going from Resort to Park by using a rental car. In fact, there are times when driving will take you much longer, namely for the Magic Kingdom.
Other advantages include:
Bus is already cooled off... no hot car to go back to.
Bus load zones are clearly marked, and close by... no schlepping through huge parking lots, searching through a hundred similar rental cars.
Leave the driving to us... no need to battle traffic, or idiot drivers. And beleive me, they are out in full force.
However, renting a car will provide you with more flexibility. You can go resort hopping, and drive off property. Downsides include having to deal with idiot tourist drivers (and there are PLENTY), and tons of traffic during park exits. Also, you have to wait in the HUGE line for the Monorail or Ferryboat at the MK, in addition to the Tram line at every park.