Ive been researching this for a while now as will be in same situation in September!
Public buses are possible, but from what i understand you'll need to go from your resort via the buses to DTD westside, then take the Lynx no.50 to SW from the Westside stop, then switch again opposite SW to another bus (or possibly the i-ride, i forget) and up and on to US/IOA. Obviously this saves a lot of money but is gonna eat up a lot of vacation time!
We're planning on bussing to Seaworld as that seems quite straightforward, but grabbing the Mears shuttles from outside the resort to get to US, IOA and also to meet up for the Busch shuttle. They were about $15-18 pp both ways last time i was there.