How soon after a bone marrow biopsy could the diagnosis of leukemia be made?

Depends / 1 week. It depends. If the bone marrow is "packed" with cancer cells it may be obvious on an initial review by a hematologist and/or hematopathologist. However, for a new diagnosis i generally tell patients it may potentially be a week for special stains/studies and "send out" studies to fully characterize the bone marrow.
Same day, but... Looking at the sample under the microscope with no special testing or staining, one can sometimes make the diagnosis of leukemia the same day. Many times, however, special testing and staining may be required. Depending on who is doing the testing, this can take 2-7 days.