Is the script only ever intended to run one minute after boot up, or can it be used at other times, too? In the former case, you can add sleep 60 to the beginning of your script, or in the latter case, add it to the crontab file:
@reboot sleep 60 && my_script.sh
As has been pointed out by sr_, though, perhaps you are tackling this in the wrong way, and a proper init.d or rc.d script would be a more robust solution.
