This paper focuses on Bayesian Lamb wave-based damage localization in structural health monitoring of anisotropic composite materials. A Bayesian framework is applied to take account for uncertainties from experimental time-of-flight measurements and angular dependent group velocity within the composite material. An original parametric analytical expression of the direction dependence of group velocity is proposed and validated numerically and experimentally for anisotropic composite and sandwich plates. This expression is incorporated into time-of-arrival (ToA: ellipse-based) and time-difference-of-arrival (TDoA: hyperbola-based) Bayesian damage localization algorithms. This way, the damage location as well as the group velocity profile are estimated jointly and a priori information taken into consideration. The proposed algorithm is general as it allows to take into account for uncertainties within a Bayesian framework, and to model effects of anisotropy on group velocity. Numerical and experimental results obtained with different damage sizes or locations and for different degrees of anisotropy validate the ability of the proposed algorithm to estimate both the damage location and the group velocity profile as well as the associated confidence intervals. Results highlight the need to consider for anisotropy in order to increase localization accuracy, and to use Bayesian analysis to quantify uncertainties in damage localization.