If you can develop your thumb and little finger on both hands, you will find the job a bit easier. On the fingering hand, the thumb acts as the bass string barre, and can damp the A if necessary. The ability to bend your index finger backwards a little (for instance), can barre notes on the treble strings.
The little finger on the fretboard hand can cover notes while another finger can get into place for the next note.

B.