Production

The production of blood cells in bone marrow begins roughly 4-5 months after conception. Stem cells immigrate from the liver into the bone marrow, where the "microenvironment" is decisive for the development of stem cells. This stroma consists of endothelial cells, fat cells, osteoblasts and fibrocytes. Here, among others, mature the B lymphocytes.
Macrophages also colonize the stroma, but they stem from hematopoietic stem cells. This creates an environment that, according to need, stimulates the proliferation and differentiation of the precursor cells. As soon as these cells are mature they proceed through the openings in the sinusoids from the bone marrow into the blood stream.

BONE MARROW

In humans and mice, bone marrow is the site of B-cell origin and development. Arising from lymphoid progenitors, immature B cells proliferate and differentiate within the bone marrow, and stromal cells within the bone marrow interact directly with the B cells and secrete various cytokines that are required for development. Like thymic selection during Tcell maturation, a selection process within the bone marrow eliminates B cells with self-reactive antibody receptors. Bone marrow is not the site of B-cell development in all species. In birds, a lymphoid organ called the bursa of Fabricius, a lymphoid tissue associated with the gut, is the primary site of B-cell maturation. In mammals such as primates and rodents, there is no bursa and no single counterpart to it as a primary lymphoid organ. In cattle and sheep, the primary lymphoid tissue hosting the maturation, proliferation, and diversification of B cells early in gestation is the fetal spleen. Later in gestation, this function is assumed by a patch of tissue embedded in the wall of the intestine called the ileal Peyer’s patch,which contains a large number B cells.

Source: Tulane University

Link: www.tulane.edu

References:

[1]  17.2 Lymphatic tissue, Human Embryology, Organogenesis from www.embryology.ch

[2] Kuby, 5^th edition, Unit 2: Cells and organs of immune system, pg 45-46, Immunology.