This question is similar to sudo in php exec() and they did not arrive at a conclusion.
In your case, since only one bash script needs to be executed in this fashion, considering using setuid instead:
$ su
[enter password]
chown root:root something.sh
chmod 4755 something.sh
exit
Note: Some Linux distributions disable setuid for shell scripts by default for security reasons.
Update: Apparently no commonly used Linux distribution today allows setuid on shell scripts. Perl used to be the exception, but suid-perl is now deprecated.
The only way to execute your bash script using this method is to invoke it from a compiled binary. See the example with the C code on how to do this.