How to check if a filesystem is mounted with a script

Many Linux distros have the mountpoint command. It can explicitly used to check if a directory is a mountpoint. Simple as this:

#!/bin/bash    
if mountpoint -q "$1"; then
    echo "$1 is a mountpoint"
else
    echo "$1 is not a mountpoint"
fi

You can check the status code of mount, and most well written executables, with the shell special parameter ?.

From man bash:

? Expands to the exit status of the most recently executed foreground pipeline.

After you run the mount command, immediately executing echo $? will print the status code from the previous command.

# mount /dev/dvd1 /mnt
  mount: no medium found on /dev/sr0
# echo $?
  32

Not all executables have well defined status codes. At a minimum, it should exit with a success (0) or failure (1) code, but that's not always the case.

To expand on (and correct) your example script, I added a nested if construct for clarity. It's not the only way to test the status code and perform an action, but it's the easiest to read when learning.

#!/bin/bash
mount="/myfilesystem"

if grep -qs "$mount" /proc/mounts; then
  echo "It's mounted."
else
  echo "It's not mounted."
  mount "$mount"
  if [ $? -eq 0 ]; then
   echo "Mount success!"
  else
   echo "Something went wrong with the mount..."
  fi
fi

For more information on "Exit and Exit Status", you can refer to the Advanced Bash-Scripting Guide.

One more way:

if findmnt ${mount_point}) >/dev/null 2>&1 ; then
  #Do something for positive result (exit 0)
else
  #Do something for negative result (exit 1)
fi