Rent the car.
Noobs to the USF/IOA world stay at Disney and only visit for a day. That's ok, you'll come over to the fun side. There's this unwritten thing that Disney people can't visit USF/IOA, but that's totally wrong, and you'll see it soon.
The shuttle situation is also another thing that needs to be addressed. Since USF/IOA and Disney don't get along, there is no shuttle between the two.
Most people who stay at USF/IOA buy the 5 park pass, which includes WnW, SWF, and BGT. You need a rental car to hop between these parks, and it's well worth it because you can visit a grocery store.
Just face it. Disney and IOA/USF hate each other. The members of this forum, and the park, stay seperate.
I post here often, but never venture to the Disney side of this forum. They stay seperate. I visit Disney every 4 years after they add a roller coaster.