  We compute power corrections to mean values of hadronic event shapes - the
thrust and the C parameter - of tagged b quark events in electron positron
annihilation, using the dispersive approach. We find that the leading power
corrections are of the same type of 1/Q corrections as for event shapes in the
massless case, with the same non-perturbative coefficient times a
perturbatively calculable mass-dependent coefficient. The effect of the mass
correction in the power correction is to reduce the latter by 10-30% for tagged
b events, for centre-of-mass energies ranging from the Z peak down to 20 GeV.
