By default, *.sh files are opened in a text editor (Xcode or TextEdit). To create a shell script that will execute in Terminal when you open it, name it with the “command” extension, e.g., file.command. By default, these are sent to Terminal, which will execute the file as a shell script.
You will also need to ensure the file is executable, e.g.:
chmod +x file.command
Without this, Terminal will refuse to execute it.
Note that the script does not have to begin with a #! prefix in this specific scenario, because Terminal specifically arranges to execute it with your default shell. (Of course, you can add a #! line if you want to customize which shell is used or if you want to ensure that you can execute it from the command line while using a different shell.)
Also note that Terminal executes the shell script without changing the working directory. You’ll need to begin your script with a cd command if you actually need it to run with a particular working directory.