Should I save my scripts with the .sh extension?

No, it is not a good practice, you should keep your scripts without extension. Note, that scripts being part of packages doesn't have a .sh extension, i.e. update-grub, not update-grub.sh. If you are still not convinced, then be advised, that Google Shell Style Guide says:

Executables should have no extension (strongly preferred) or a .sh extension. Libraries must have a .sh extension and should not be executable.

PS You don't have to put your script into /bin. You can create directory ~/bin and put your script there. Directory ~/bin is included in $PATH by default, so scripts put there can be run as any other shell command.

I second the recommendation to use ~/bin which gets automatically added to your $PATH,as Sergey said. Or /usr/local/bin, which may already be on the PATH. However:

• You are doing this for yourself. Use whatever you feel comfortable with. Indeed, I'd say keep the extension so that you'll be reminded it's your script you are running, since -

• Extensions are uncommon in /usr/bin. In my system, I can find only two:

  $ dpkg -S `ls /usr/bin/*.sh`
  mtools: /usr/bin/amuFormat.sh
  gettext-base: /usr/bin/gettext.sh
  

  So if you are packaging, definitely leave out the extension.

Just put following line at top of file:

#!/bin/bash

So-that file will be automatically type : Shell Script without any extension!

Remember to give execution permission to file.

For putting script so-that can be run by direct command, visit: Where should I put my script so that I can run it by a direct command?