So what would be the best way to approach 'My One and Only Love'? It loses a lot played up an octave. should I tryYes, we tend to forget that the Realbook in Bb is also meant for trumpets and clarinets, which both go down to low A and more.
In such cases, you could either modify the low A (or other out of range note) by moving it to another chord tone, shifting the whole phrase. part of it or just the note itself up an octave, or standing on the previous note, depending on what works best in the actual context of the tune.
You wouldn't just play one note up an octave, but an entire phrase/line. Although, sometimes the entire melody is written an octave lower from where it is played.I'm pretty sure I've even seen low A's in the Eb Real Book (Vol. 5, if I recall correctly). I think "In A Sentimental Mood" has one thrown in somewhere... And I know there aren't trumpet players using that! When I've needed to play it I would play the higher A, but that never really sat right with me.