Can someone detect bone cancer through a blood test?

Depends: Some blood tests will suggest or prove certain kinds of bone cancer, for example multiple myeloma is a bone disease in whcih the tumor cells are plasma cells which often secrete a protein which can be found in the blood. Many kinds of bone cancer are not identifiable by a blood test.

Maybe soon: At this point, it is not possible though there are some newer technologies that may make it possible to detect circulating tumor cells or a signature for having a bone cancer like osteosarcoma or ewing sarcoma.