Create a group, for example "accounting".
Add whatever users you want to the "accounting" group. Example code:
# for i in $(cat accounting_users.txt); do
usermod -G accounting $i
Change ownership of the script so it belongs to that group:
# chgrp accounting /path/to/script.sh
chmod the file so that only users from that group can run it:
# chmod 750 /path/to/script.sh