Legionnaire, I don't think there is any double decker bus that goes to Changi. What I can suggest is catching a train or taking a cab into town for some breakfast, then maybe a walk around, and the bus ride, and then train/cab back to the airport. Squeezing the zoo or the birdpark into the day is probably a bit too tight for comfort.
Why don't you consider taking the open top double decker hop-on/off tour buses? It's called HiPPOTours in Singapore, they are run by the same people that do the DuckTours (
www.ducktours.com.sg). However, I can't seem to find a website for the HiPPOTours.