The detection reagent B should be the detection AB ( HRP-conjugated Streptavidin-antibody).
Streptavidin binds to biotin with high affinity. Streptavidin-HRP is useful for detecting biotinylated antibodies, e.g., in ELISA. For ELISA applications, HRP will act on soluble substrates, such as the TMB, to yield a colorimetric reaction.
Oops, I thought this was the A reagent. What is than the A reagent?
Because in the first step (see procedure) you already have the sample. This binds on the AB on the well. And than A binds to the sample. So I don't know the function of B.
Solution A is most likely the 2nd antibody in a sandwich ELISA (the plate has been pre-coated with the capture antibody). If A is biotinylated, B is very likely streptavidin-HRP. B also could be a peroxidase coupled antibody that recognizes the species of A.