I bought the fruit and I have my Chocobo in a stable and I know I'm suppose to feed him the fruits in a order (e.g. if I have 10 pears 10 apples and 10 oranges instead of feeding him 10 apples then 10 pears and finally 10 oranges, I'd feed him 1 apple 1 pear and 1 orange then repeat... But the question I have is can I feed him all the fruit in one sitting because the phrase "Chocobo Plumage will be ready for change in 6 hours" after I gave her one fruit.
Yes you can feed them all within the same 6 hours. When you get the message about color being ready in 6 hours it doesn't mean the color will change. The color will change when you get the message {Chocobo's name/ plumage will change in 6 hours}. You can still feed past this message as well to keep moving towards the color you want. Also you have to leave your chocobo in the stable for the whole 6 hours, if you take it out early no change will happen.
Also you might want to use Sadana's advice here to help with the big move at the beginning.
http://forum.square-enix.com/ffxiv/threads/203825-chocobo-color-question?p=2578405#post2578405
There's a calculator online that I've found works 100% of the time. Here ya go, click this link.