Sounds like a permission issue.
Does the user have writes to the directory containing the script ?
Is the user in the same group as the group of the script ?
It works when you grant root permissions (SU) because that user has access to all.
Login as the user in question and -->
joe@Tux-Box ~]$ id
uid=1000(joe) gid=100(users) groups=100(users),0(root),7(lp),10(wheel),50(games),91(video),92(audio),93(optical),98(power)
Does the above match the group below (users in my example)
[joe@Tux-Box ~]$ ls -l ~joe/Scripts/BU
-rwxr-x--- 1 joe users 5511 Apr 12 20:25 /home/joe/Scripts/BU
What is the second set of permission show on the file and the directory it is contained in ?
[joe@Tux-Box ~]$ ls -ld ~joe/Scripts/
drwxr-xr-x 4 joe users 4096 Apr 29 18:58 /home/joe/Scripts/
If you are still stuck post your results of the above and we can take it from there.
Hope this helps.