will decomp from a small bird cause a lot of stink if it’s not buried deep enough?

i linked the post explaining what happened. if you can’t be bothered to read the post: i am not keeping it!! i know its illegal!!

i buried the bird in my backyard in an inconspicuous spot but i couldn’t dig very deep. i didn’t have a shovel to use so i did it with my hands and a stick.. maybe a foot deep.

there’s no head, a lot of the organs were gone from what i could tell. not a ton of flesh. it almost looked hollowed out but i didn’t want to touch it too much even with gloves. should i be worried about a smell? i personally don’t care, i just don’t want to explain to my dad that the stink is coming from the hole i dug in his yard to bury a dead bird cause i’m too sensitive to throw it in the garbage.