[bash] How can I count the occurrences of a string within a file?

I'm taking some guesses here, because I don't quite understand what you're asking.

I think that what you want is a count of the number of lines on which the pattern 'echo' appears in the given file.

I've pasted your sample text into a file called 6741967.

First, grep finds the matches:

james@Brindle:tmp$grep echo 6741967 
    echo "Preparing to add a new user..."
echo "1. Add user"
echo "2. Exit"
echo "Enter your choice: "

Second, use wc -l to count the lines

james@Brindle:tmp$grep echo 6741967  | wc -l
       4