See, suppose the vertex set={$1,2,3,4,5$}
Edge-set={$(1,2)$,$(1,3)$,$(2,4)$,$(3,5)$}
On applying BFS, you would see that the color of 1 is red, of 2 and 3 is black,4 and 5 is red.
Therefore the partite sets are :-{$1,4,5$} and {$2,3$}.
How many possible edges can be there between these partite sets ? |{$1,4,5$}| $\times$ |{$2,3$}|=
$3 \times 2 =6$.
Number of edges already existing in the bipartite graph=|Edge-set|=4.
How many edges can we add ? 6-4=2.
Please comment if some part is still unclear.