Birds normally don't die close to your house. But it happens. Usually they get far away from any activity and "become part of the food chain" with help from some scavenger.
But in case you run across a dead bird, how you handle it is your choice; the bird won't care. Burying it in the ground is about your emotions and traditions. This may prevent disease, but a raccoon (or other scavenger) may dig it up. A better way is double-bag the carcass and simply put it in an outdoor garbage can.