The process in which immature B cells from the bone marrow become mature B cells in the spleen. Transitional stage B cells are subdivided into transitional one (T1) and transitional two (T2) stages and are short-lived and functionally incompetent.
Comment:
Note that immunologists typically use the word 'development' to refer to cells of B or T cell lineages undergoing the process that GO describes as 'cell differentiation'.