No, Bell inequalities do not favour Bohmian mechanics over other interpretations of QM. However, the experimental violations of Bell inequalities rule out any hidden variable theory that does not share some of the key features of Bohmian mechanics, indeed, first and foremost the non-locality.
With a bit more details, Bell inequalities are theorems which apply to hidden variable theories. Consider the famous experiments with entangled pairs of particles: when one member of the pair is observed with a spin +1, the other is always observed with a spin -1. There are two premises to demonstrate Bell inequalities: (i) each pair is produced in a well-defined state and keeps that state until measurement (i.e. one particle has a spin +1 and the other one has a spin -1, always), and (ii) the measurement on one particle is totally independent from the measurement on the other particle. Since Bell inequalities have been observed to be violated, either (i) or (ii), or both, are false. Those people who are attached to the metaphysical concept of a reality independent of our observing it definitively want to keep (i) and therefore they have to accept that (ii) is false. But then Bohmian mechanics precisely provide such an escape. Bell himself wrote that he felt vindicated when he read Bohm's seminal article, actually.
On the other hand, interpretation of QM are just that interpretations: they make the exact same predictions and they share common features essential to derive those predictions. Non-locality is one of them: it is inescapable and Bohmian mechanics is non-local in exactly the same way as the Copenhaguen interpretation since in both cases the non-locality comes from the wave function dependence on the positions, spins, etc of all the particles in the system under scrutiny. There is really no difference at that level between both interpretation.