In this paper, we develop a general Bayesian hierarchical model for bridging across patient subgroups in phase I oncology trials, for which preliminary information about the dose-toxicity relationship can be drawn from animal studies. Parameters that re-scale the doses to adjust for intrinsic differences in toxicity, either between animals and humans or between human subgroups, are introduced to each dose-toxicity model. Appropriate priors are specified for these scaling parameters, which capture the magnitude of uncertainty surrounding the animal-to-human translation and bridging assumption. After mapping data onto a common, 'average' human dosing scale, human dose-toxicity parameters are assumed to be exchangeable either with the standardised, animal study-specific parameters, or between themselves across human subgroups. Random-effects distributions are distinguished by different covariance matrices that reflect the between-study heterogeneity in animals and humans. Possibility of non-exchangeability is allowed to avoid inferences for extreme subgroups being overly influenced by their complementary data. We illustrate the proposed approach with hypothetical examples, and use simulation to compare the operating characteristics of trials analysed using our Bayesian model with several alternatives. Numerical results show that the proposed approach yields robust inferences, even when data from multiple sources are inconsistent and/or the bridging assumptions are incorrect.