The lifetimes of the B+ and B0 mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z0 decays recorded at LEP. Z0 -> b bbar decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructed charged and neutral secondary vertices selected in this tagged data sample. The results are tau(B+) = 1.643 +- 0.037 +- 0.025 ps tau(B0) = 1.523 +- 0.057 +- 0.053 ps ratio tau(B+)/tau(B0) = 1.079 +- 0.064 +- 0.041 where in each case the first error is statistical and the second systematic. A larger data sample of 3.1 million hadronic Z0 decays has been used to search for CP and CPT violating effects by comparison of inclusive b and bbar hadron decays. No evidence for such effects is seen. The CP violation parameter Re(epsilon_B) is measured to be Re(epsilon_B) = 0.001 +- 0.014 +- 0.003 and the fractional difference between b and bbar hadron lifetimes is measured to be -0.001 +- 0.012 +- 0.00
