You do most things in bash by issuing commands like cp. Most of these commands are small programs, though some, like cd are built into the shell.
The commands come in packages, most of them from the Free Software Foundation (or GNU). Rather than list the packages here, I'll direct you to the Linux From Scratch HOWTO. It has a full and up to date list of the packages that go into a Linux system as well as instructions on how to build them.