This paper estimates bowhead whale locations and uncertainties using non-linear Bayesian inversion of their modally-dispersed calls recorded on asynchronous recorders in the Chukchi Sea, Alaska. Bowhead calls were recorded on a cluster of 7 asynchronous ocean-bottom hydrophones that were separated by 0.5-9.2 km. A warping time-frequency analysis is used to extract relative mode arrival times as a function of frequency for nine frequency-modulated whale calls that dispersed in the shallow water environment. Each call was recorded on multiple hydrophones and the mode arrival times are inverted for: the whale location in the horizontal plane, source instantaneous frequency (IF), water sound-speed profile, seabed geoacoustic parameters, relative recorder clock drifts, and residual error standard deviations, all with estimated uncertainties. A simulation study shows that accurate prior environmental knowledge is not required for accurate localization as long as the inversion treats the environment as unknown. Joint inversion of multiple recorded calls is shown to substantially reduce uncertainties in location, source IF, and relative clock drift. Whale location uncertainties are estimated to be 30-160 m and relative clock drift uncertainties are 3-26 ms.