naive b cells

[forchina]

How long does it take for a naive B cell's antibodies to bind with its specific antigen?

[simpak]

So you should really specify that it's on the surface and not in the serum when you're talking about antibody from a naive B cell.
It depends on how long it takes the antigen to be processed and carried to the lymph node by antigen presenting cells.  It's all really just 'a matter of chance' - the APC will move throughout the lymphatics and present antigen to different cells in different nodes until one binds to the antigen and becomes activated.  So nobody really knows how long, but usually it takes around 5 or so days to mount an adaptive immune response.