do shell script "sh /Volumes/Media/~Users/me/Software/StartKeepass.sh" user name "<enter username here>" password "<Enter password here>" with administrator privileges
Right-click the file in Finder, and click the "Get Info" option.
At the bottom of the window, set the shell script to open with the terminal.
Now when you click on the script in the dock, A terminal window will pop up and execute your script.
Bonus: To get the terminal to close when your script has completed, add exit 0 to the end and change the terminal settings to "close the shell if exited cleanly" like it says to do in this SO answer.