This is a question with no one right answer, but if I were doing this, I might consider starting the second season with Character B and continuing up to the point where he meets Character A, and then backtracking to fill in on Character A.
The advantage is that Character B gets a strong solid uninterrupted block of narrative to establish himself. The disadvantage is that it may turn off readers who are already invested in Character A.
One way to address the new disadvantage would be to wait until the moment they meet to do Character B's story (as a flashback). Conversely, you could do Character B's story first, but add some foreshadowing of the importance he will have to Character A (i.e. have them visit the same locations, or pass each other on the street, etc.)