I do really appreciate the solution you came up with, and I guess there's no way around it straight with bash. Here's the little point you've missed:
BASE62=($(echo {0..9} {a..z} {A..Z}))
for i in $(bc <<< "obase=62; 9207903953"); do
echo -n ${BASE62[$(( 10#$i ))]}
done && echo
Output:
a39qrT