was it the benny goodman band which backed her ?
No, this was Martha Tilton and her VDisc Playfellows: Billy Butterfield (trump), Vernon Brown (tromb), Joe Dixon (clairn), Nick Calazza (ten sax), Billy Rowland (piano), Hy White (guit), Felix Giobbe (bass), George WEttling (drums), and arrangement by Sy Oliver. :)
except billy butterfield, geoge wettling and, of course, sy oliver I did not know those musicians but they seem very good especially the guitarist.
I have a few more by them with Martha, from VDisc, that will be on the lists of what I have of hers :)