Yujade that is a great idea:)
Neri, If you haven't got much luggage (i.e just a back pack to take with you that would work out the best option.
Otherwise if you need to get back to Chengdu by 4.30 you will be cutting it fine.
The Panda centre opens at 8am & they start feeding the Pandas at 8.45 approx. The quickest way to get around & see everything is get on one the Panda Centre guides.
There is a building on the left hand side, just after the entrance. The guides there are terrific & it only cost RMB100. Quite often you will get one of the animal caring staff, such as someone doing there PHd and they know all the in's & outs of the centre & can get you to the right place quickly to watch the Pandas feed.
Also get one of the motorized carts at the entrance. That will save you 12 minutes instead of walking to the first enclosure.
You should be finished at 10.30 - 11am.
If catching a bus make sure you get an express one to Leshan and back to Chengdu. Keep in mind for your return journey that most buses will not leave until full. So even if it is supposed to leave at a certain time you might get a bus that won't budge until all seats are taken.
The Panda Centre and Leshan can be done in one day but it might be a bit nerve wrecking if you have to be back in Chengdu by 4.30pm. It also will not give you long enough in Leshan to have a good look around.
Doing as Yujade suggested will save you time rather than heading all the way back to Chengdu & then out to the airport.