Re: An easier way to play a B flat to and A in a run quickly.
1) Practice going back and forth between B flat and A, using the standard fingerings. Practice with a metronome starting out very slowly and very very gradually working up the speed. Make sure that your fingers don’t fly too high above the recorder. Practicing in front of a mirror can help you monitor this.
2) If the run goes quickly, you might consider using a trill fingering for the B flat to A. Assuming you play treble/alto, this would involve cheating on the B flat and fingering it T 1 2 3 4 instead of the standard T 1 2 3 4 6 7 (or T 1 2 3 4 6 in the second octave). The A will use the standard fingering. Trilling this way between the B flat and the A simply involves raising and lowering the 5th finger. The B flat will be slightly sharp, but who cares since, given the situation, it’s close enough for government work.
If you’re not yet familiar with this site, http://www.recorder-fingerings.com/en/index.php offers a wealth of information on recorder fingerings.
All the best.
–Dick–