No, bash is not a monad. Really. This sort of article tends to obscure more than it illuminates.

Bash runs the commands of a pipeline in parallel, so you don't get the sequencing of side-effects that monads provide. You'd better off saying that shell commands are plain functions (mapping stdin to stdout) than insisting they're Kleisli arrows.

But to play along with the conceit: the pipe operator would translate into the >=> operator, not >>=. The first command in the pipeline has a stdin, it's just that usually the first command in a pipeline is one that ignores its stdin.