In hadronic decays of Z bosons recorded with the OPAL detector at LEP, events of b quarks were selected using the long lifetime of b flavoured hadrons. Comparing the 3-jet event rate in b events with d,u,s and c quark events, a significant difference was observed. Using O(alpha**2) calculations for massive quarks, the b quark mass was determined in the MSbar renormalisation scheme at the scale of the Z boson mass. By combining the results from seven different jet finders, a single value for the running b quark mass was determined.