Perhaps a short alternative version (No "Series bug" detected)
Normal[Series[
A /. Thread[Variables[A] -> eps Variables[A]], {eps, 0, 1}]]
/.eps -> 1 (* -1 + a + b*)
Normal[Series[
B /. Thread[Variables[B] -> eps Variables[B]], {eps, 0, 1}]] /.
eps -> 1 (* a *)