The normal way of doing this is to write the process id into a file. The first thing the script does is check for the existence of the file, read the pid, check if a process with that pid exists, and for extra paranoia points, if that process actually runs the script. If yes, the script exits.
Here's a simple example. The process in question is a binary, and this script makes sure the binary runs only once. This is not exactly what you need, but you should be able to adapt this:
RUNNING=0
PIDFILE=$PATH_TO/var/run/example.pid
if [ -f $PIDFILE ]
then
  PID=`cat $PIDFILE`
  ps -eo pid | grep $PID >/dev/null 2>&1
  if [ $? -eq 0 ]
  then
      RUNNING=1
  fi
fi
if [ $RUNNING -ne 1 ]
then
    run_binary
    PID=$!
    echo $PID > $PIDFILE
fi
This is not very elaborate but should get you on the right track.