If you're sure it's bone, then I would say these are bullet holes. Back in the day, I would toss sun-dried bones in the air and shoot them with my Ruger .22 pistol (I wasn't always the brightest bulb in the lamp). The holes look very similar.
You may wish to take it to the Anthropology Department at Miami U (my alma mater) and ask them to ID your find. The school may be closed, call first.
Don.....
PS: Welcome to treasurenet !!
sand chip nailed it(atleast what the material is). that's a piece of porcelain. you can clearly see the glaze and also uniform structure in the breaks.