An activated B cell responds in similar fashion to Th or Tc cells. The few cells responding to an antigen proliferate into large clone populations. These are large cells with a lot of cytoplasm and are entirely given over to producing antibodies. These antibodies are released into the blood stream to be carried to the site of infection. The B cells themselves do not migrate to an infection site, it would be a waste of time and energy and they would get in the way.
Antibodies are the long distance smart bombs of the immune system.
They diffuse throughout the entire body and only bind to the particular antigen they were made for. A few of the clone cells that result from antigen activation become memory cells. APCs are a heterogeneous population of cells sourced from cells of both the innate and adaptive immune systems. Most APCs are probably derived from the phagocytic line but we are not really sure. Clearly B cells are a very different cell type, not phagocytic at all, and there may be other different cell populations.