Here is a complete bash script that meets the requirements:

#!/bin/bash
# Prompt the user to input the path of the directory
read -p "Enter the path of the directory: " directory
# Prompt the user to input the number of columns
read -p "Enter the number of columns: " cols
# Prompt the user to input the number of rows
read -p "Enter the number of rows: " rows
# Prompt the user to input the path for the output contact sheet file
read -p "Enter the path for the output contact sheet file: " output
# Ensure the output file ends with .jpg
if [[ ${output##*.} != "jpg" ]]; then
    output="${output}.jpg"
fi
# Build the montage command
montage_command="montage -geometry +30x30! -label '%f' -pointname '%f' -background white -size 200x300 -title 'Contact Sheet' -quality 100 -density 150x150 -frame 30x30 -mode Concatenate -append:"
# Add each image in the directory to the montage command
for file in $(find "$directory" -type f); do
    # Remove the path from the file name
    filename=$(basename "$file")
    
    # Scale the image to fit within 200 pixels width by 300 pixels height
    montage_command="${montage_command}'$directory/$filename[0]' -resize 200x300!"
    
    # Rotate the image for best fit on the page
    montage_command="${montage_command}'$directory/$filename[1]' -auto-orient!"
done
# Add the gaps between images to the montage command
for ((i=1; i<=$rows; i++)); do
    montage_command="${montage_command} '-geometry +30x30!'"
done
for ((i=1; i<=$cols; i++)); do
    montage_command="${montage_command} '-geometry +30x30!'"
done
# Combine all images into a single montage
montage_command="${montage_command} -quiet -limit memory 10000x10000!"
# Run the montage command
echo "$montage_command > $output"

Save this script in a file with a .sh extension (e.g. contact_sheet.sh), make it executable with chmod +x contact_sheet.sh, and run it with ./contact_sheet.sh.