Just my opinion, but...
We have stayed at BC several times (BC is our home resort), and have NEVER rented a car. We've always taken the shuttle. I will be the first to admit that the shuttle is probably not condusive to everyone's lifestyle, but it has never steered us wrong.
You will receive a bus schedule when you check in that lists all the drop-off and pick-up times from each of the parks. In the mornings, MK and Epcot are combined on one bus on the hour and half-hour (e.g. 8am, 8:30am, 9am...through 12 noon). AK and DHS are a combined route, leaving BC in the am on the :15 and :45 of the hour.
We found that the bus schedule mostly worked for us. There have been a few times over the years that we have jumped in a cab if the bus schedule just wasn't working for us, but that has been few and far between.
Of course, if you are more of a "fly by the seat of your pants" family, you might be more comfortable renting a car. But if it doesn't play a big part in the enjoyment of your vacation, then I wouldn't bother.