What is the relationship between taking vitamin b-12 and the likelihood of getting blood clots?

Low or unrelated. Cyanocobalamin or vitamin B12 is important for normal erythrocyte formation (red blood cell). If b 12 is deficient, one gets pernicious anemia and the mean corpuscular volume (MCV) climbs > 100. Gastric bypass, gastric resection surgeries increase the risk of pernicious anemia. But as to increased risk for DVT or deep venous thrombosis ("blood clots") vitamin B12 palys little if any role.
Pro clot. Too much B12 can lead to a clot. If you don't need it for a deficiency then stop.