In Bohmian mechanics there is no collapse. Each particle has a definite position guided by the pilot wave, which is essentially the wave function of traditional QM. This wave function never collapses.
However, over time certain parts of the wave function become irrelevant, as they deal with configurations of the system far from the actual, definite configuration. Accordingly the system's actual configuration will never again be affected by these parts of the wave function. If we are doing a calculation we can forget about these parts of the wave function, or set them to zero. Doing so is exactly the same thing as collapsing the wave function in traditional QM.