I would take a guess that this was part of an instinct that is no longer useful to the domestic dog.
Wild canids will bury excess food away from the site of a kill to save for leaner times and to lessen the risk of scavengers finding it. Your dog has lost most of this instinct as it is not needed in the domestic situation but is still displaying part of it.
Pretty cute - you should tell all your friends that you have taught her to feed the birds!!!!