Welcome Guillermo.
DOS is a Disk Operating System. It is a software that interfaces with a computer's hardware to make it do things.
DOS is old, used back when personal computers had little memory and sometimes no hard drives, and the DOS resided on a floppy diskette.
BASH is the Bourne Again SHell. It is a command-line interface between a Unix-type operating system and the user.
Originally, Unix was installed in mainframe computers: machines that took up entire rooms. There was a command-line feature called the Bourne Shell which allowed users to interface with the mainframe operating system.
BASH is basically a reverse-engineered copy of that shell designed to interface with Unix-analogues built to run on desktop/personal computers such as GNU/Linux and nowadays MacOS (I believe there is a version for Windows 10 now).
Both are command-line interfaces, though the command sets are different between the two.
Microsoft killed their MS-DOS in the mid-90s when Windows 95 came out. There other DOSes out there, but I couldn't tell you how well they will run on modern processors.
BASH and its analogues are found in any Unix-like operating system.
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