How do you tie to the buoy?
We use a warp from the bow D ring to the chain attached to the mooring buoy.
Most mooring chains will have a loop where they attach to the buoy.
We take two tight turns around the loop in the chain with the warp and then two or three half hitches to secure. This avoids the warp chafing on the chain and is more secure than a warp looped through the chain loop and back to the boat.
Any remaining warp can be made back to the boat if long enough, but make sure there is no load on this end of the line.