It will depend on each situation as well as exactly where you room is located at the Caribbean Beach. If your closest bus stop is one of the first to be picked up, that means you will have to sit through all the rest of the Caribbean internal bus stops until you actually leave the grounds. That's not going to save you that much time. However, if your closest bus stop is one of the last to be picked up, you will leave for the park almost immediately. Of course, if you are one of the first to be picked up, you will probably get a seat but if you are one of the last to be picked up, you will probably have to stand. That should factor into your decision especially if you have a problem with anyone in your party standing on a bus. Never assume you will get a seat because you are small, or have a medical condition. Life on Disney buses will be a lot easier for you that way.
If you drive, unless you get to the park fairly early, you will have to take a tram to the front of the park. That means more time spent in the parking lot waiting for the tram (they are usually fairly quick though) and then going to the front. If you decide to walk, count in that walk time. And then reverse everything when leaving the park. And don't forget about having to stop at the parking booths so they can see your resort pass for free parking. If the park is a popular one that day, that will cost you time as you wait for each car to get recognized.
If you drive, you will have to know your way around Disney property so study the maps before you set out. Disney World is huge and if you've never driven before, give yourself some extra time in case you get lost.
There are tons of different ways to get around Disney World. We use a variety of transportation options. Car, bus, boat, monorail, foot. We get creative and have had some of our best moments using odd combinations to get around.