The first argument to Popen is a list containing the command name and its arguments. > is not an argument to the command, though; it is shell syntax. You could simply pass the entire line to Popen and instruct it to use the shell to execute it:
process = subprocess.Popen(bashCommand, shell=True)
(Note that since you are redirecting the output of the command to a file, though, there is no reason to set its standard output to a pipe, because there will be nothing to read.)
A better solution, though, is to let Python handle the redirection.
process = subprocess.Popen(['pdfcrack', '-f', 'pdf123.pdf'], stdout=subprocess.PIPE)
with open('myoutput.txt', 'w') as fh:
for line in process.stdout:
fh.write(line)
# Do whatever else you want with line
Also, don't use str.split as a replacement for the shell's word splitting. A valid command line like pdfcrack -f "foo bar.pdf" would be split into the incorrect list ['pdfcrack', '-f', '"foo', 'bar.pdf"'], rather than the correct list ['pdfcrack', '-f', 'foo bar.pdf'].
>is also a filename. Try writing to a file with python using the stdout