automate gnuplot plotting with bash

If I understand correctly, this is what you want:

for FILE in *; do
    gnuplot <<- EOF
        set xlabel "Label"
        set ylabel "Label2"
        set title "Graph title"   
        set term png
        set output "${FILE}.png"
        plot "${FILE}" using 1:2:3:4 with errorbars
EOF
done

This assumes your files are all in the current directory. The above is a bash script that will generate your graphs. Personally, I usually write a gnuplot command file (call it, say, gnuplot_in), using a script of some form, with the above commands for each file and plot it using gnuplot < gnuplot_in.

To give you an example, in python:

#!/usr/bin/env python3
import glob
commands=open("gnuplot_in", 'w')
print("""set xlabel "Label"
set ylabel "Label2"
set term png""", file=commands)

for datafile in glob.iglob("Your_file_glob_pattern"):
    # Here, you can tweak the output png file name.
    print('set output "{output}.png"'.format( output=datafile ), file=commands )
    print('plot "{file_name}" using 1:2:3:4 with errorbars title "Graph title"'.format( file_name = datafile ), file=commands)

commands.close()

where Your_file_glob_pattern is something that describes the naming of your datafiles, be it * or *dat. Instead of the glob module, you can use os as well of course. Whatever generates a list of file names, really.