B cells don't need to be activated by a Dendritic cell, they just sort of wade around the lymph nodes, checking for antigens their receptors recognize. Once they do, the B cells start producing antibodies, basically their receptors. If Helper T cells are activated, some of them will come to the B cells and "encourage" the already activated B cells so that they produce faster.
B cells also change their receptors when they multiply to see if they are better suited for the antigen. If not, they commit suicide, and once their receptors are almost perfect, they turn into Plasma cells, producing antibodies way faster.