Measurements of Rb, the ratio of the b bbar cross-section to the q qbar cross-section in e+ e- collisions, are presented. The data were collected by the OPAL experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV. Lepton, lifetime and event-shape information is used to tag events containing b quarks with high efficiency. The data are compatible with the Standard Model expectation. The mean ratio of the eight measurements reported here to the Standard Model prediction is 1.055 +- 0.031 +- 0.037, where the first error is statistical and the second systematic.