I think there is still a direct bus from Epcot to BB -- direct, but not non-stop. The bus from Epcot to CSR used to continue to BB, and I think it still does. Check with a driver at Epcot. If I'm wrong, you'll have to take the bus from Epcot to AK, and then transfer to the shuttle to BB.
If you go back to your resort, you will need to take the bus from the resort to AK to get to BB, so it will take much longer.
If you don't want to carry your swimsuits and towels around Epcot, there are coin lockers in the Epcot bus area that take 4 quarters. There's a change machine around the corner at the vending area, but it's often out of order, so you'd be wise to get the change at your resort.