The hand hand fingering for the B Flat Major scale starts on the B flat with the third finger. From there walk up the scale until your thumb hits the D and cross over with your fourth finger to hit the E flat. Your thumb will come to the A and you will cross over again and hit the final B flat with your second finger.
What finger plays B in the right hand for the C major scale?
Start with your 5th finger on the bottom C and play the next 4 notes, D, E, F, & G with your 4th, 3rd, 2nd, & 1st fingers. Next, cross over your 3rd finger to play the A, then play B with your 2nd finger and finally the top C with your thumb, or 1st finger. Again, use the same fingering coming back down the scale.