Vehicle trajectory information are becoming available from mobile sensors such as onboard devices or smart phones. Such data can provide partial information of origin-destination trips and are very helpful in solving the network flow estimation problem which can be very challenging if only link counts are used. Even with this new information, however, there is still structural bias in the maximum likelihood based approach because of uncertainties in the penetration rates. A Bayesian inference approach in which the earlier link-count-based methods are extended is proposed. We incorporate posterior simulation of route-choice probabilities and penetration rates. The results of a numerical example show that our method can infer network flow parameters effectively. Inclusion of mobile sensor data and prior beliefs based on it can yield much better inference results than when non-informative priors and only link counts are used.