What cell types produce immunoglobins and where are those cells found?
First: B cells do not produce antibodies, but rather they synthesise the B cell receptor. This may sound a bit picky, but is not, since the B cell receptor is anchored in the membrane of B cells and not secreted. Its this receptor which recognizes antigens and causes the production of highly specific antibodies (including somatic hypermutation and all related processes).

Antibodies are produced by plasma cells (and that basically the only thing they do), which are differentiated from activated B cells which have undergone the selection process on the given antigen. 
IgM is the first set of antibodies produced by the mature B cell, later on this often changes to IgG (different heavy chain, same antigen recognition site) by class switching.

The secreted antibody is IgA, which is found basically in all body fluids and is also secreted into the different mucosas of the body. It has two subtypes: IgA1 and IgA2 with A1 mostly present in the serum and A2 mostly secreted (see: "IgA subclasses in various secretions and in serum." for details).
IgA is made by plasma cells which are located in the lamina propria adjacent to mucosal surfaces. For details see thesetwo papers:


Intestinal IgA synthesis: regulation of front-line body defences.
The polymeric immunoglobulin receptor (secretory component) mediates
transport of immune complexes across epithelial cells: a local
defense function for IgA.


B cells (and also plasma cells) are found in the blood, they are then called peripheral cells. B cells have to be present outside the lymphatic tissues (not only bone marrow but also lymph nodes and the spleen) to be able to get in contact with antigens. Upon contact with an antigen they move into the adjacent lymphatic tissue.
You will not find IgG mRNA in the blood, as this will trigger immune responses. And it has no function outside of the cell.