Can specific B-cells be created in a lab?
We aren't there yet. 

There is a complex interplay between antigen recognition, presentation, and activation that would have to be worked out. You would also need to engineer the corresponding T-Cell which could recognize the antigen, become activated, which means you also need to develop a dendritic cell that can present to the T-cells, so that they could then go on to activate the B-Cells. Doing this in vitro would be a challenge.

You are actually asking to design highly specific receptors, and protein engineering then sequencing back to a genome would be difficult to do. 

If you tried taking a known antibody, you would need to track down the actual B-Cell that produces it, due to somatic hypermutation creating a unique DNA sequence, which leads to the specificity that increases the affinity of antibodies for their ligands. I guess if you did it with germ free mice, you might have a shot at isolating their B-Cells and then finding out the gene sequence. Not impossible, in my opinion, but very difficult at this point.

The closest thing I have heard of so far is the work that is being done in Dr. Carl June's lab. They are working on taking cytotoxic T-Cells, and recombining their receptor DNA so that they can then recognize a patient's tumor and kill the cancer cells, but that is a bit different than what you are asking.