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.

Here's a complete bash script that accomplishes the tasks you've outlined:

#!/bin/bash

# Prompt user for directory path
echo "Enter directory path:"
read dir_path

# Prompt user for number of columns
echo "Enter number of columns:"
read cols

# Prompt user for number of rows
echo "Enter number of rows:"
read rows

# Calculate total number of images and total width
total_images=$(ls -1 "$dir_path"/* | wc -l)
total_width=$((cols * 230)) # 200px for each image plus 30px gap

# Check if total width is greater than 300px, if so, increase rows
if (( $(($total_width / 300)) < $rows )); then
    rows=$(($total_images / $cols))
    if (( $(($total_images % $cols)) != 0 )); then
        rows=$(($rows + 1))
    fi
fi

# Calculate total height
total_height=$((rows * 300))

# Prompt user for output file path
echo "Enter output file path:"
read output_file

# Create contact sheet using Montage
montage -geometry +0+0 -label "%t" -pointsize 20 -background white \
        $(ls -1 "$dir_path"/* | sed '1d' | awk "NR==$total_images{print}") \
        -tile "$colsx$rows" -geometry 200x300\> \
        "$output_file"

echo "Contact sheet created successfully!"

Save the script as a file (e.g., contact_sheet.sh), make it executable (chmod +x contact_sheet.sh), and run it (./contact_sheet.sh). It will prompt you for the necessary inputs and create the contact sheet file in the specified output path.