Do you just want to log the scripts execution or do you want something more structured? If it's the former you can redirect the output from within the bash script with this (apologies for any condescension, I'm not familiar with your skill tree):
if [ ! -t 1 ]; then
exec > /my/log/file 2>&1
fi
The if statements tests if your at an interactive prompt, if your not all output from the script get's redirected to /my/log/file. The above poster is instead redirecting into a subprocess " > (tee)" that will both print the output and log it.
It should be noted that often the bottleneck is the terminal itself, try running your scripts with a "> /dev/null" to suppress output and verify the slow part is actually the script.
It should be noted that often the bottleneck is the terminal itself, try running your scripts with a "> /dev/null" to suppress output and verify the slow part is actually the script.