Check if Mac process is running using Bash by process name

A shorter solution:

if pgrep $PROCESS_NAME; then
    echo 'Running';
fi

Explanation:

pgrep exits with 0 if there is a process matching $PROCESS_NAME running, otherwise it exist with 1.
if checks the exit code of pgrep, and, as far as exit codes go, 0 is success.

Parsing this:

ps aux | grep -v grep | grep -c [-i] $ProcessName

...is probably your best bet.

ps aux lists all the currently running processes including the Bash script itself which is parsed out by grep -v grep with advice from Jacob (in comments) and grep -c [-i] $ProcessName returns the optionally case-insensitive integer number of processes with integer return suggested by Sebastian.

Here's a short script that does what you're after:

#!/bin/bash
PROCESS=myapp
number=$(ps aux | grep -v grep | grep -ci $PROCESS)

if [ $number -gt 0 ]
    then
        echo Running;
fi

EDIT: I initially included a -i flag to grep to make it case insensitive; I did this because the example program I tried was python, which on Mac OS X runs as Python -- if you know your application's case exactly, the -i is not necessary.

The advantage of this approach is that it scales with you -- in the future, if you need to make sure, say, five instances of your application are running, you're already counting. The only caveat is if another application has your program's name in its command line, it might come up -- regular expressions to grep will resolve that issue, if you're crafty (and run into this).

Research the Darwin man pages for ps, grep, and wc.