Now I know that I must use BASH or PERL to write an script to capture this data at the serial port and parse it.
Those are only two possibilities. There are dozens of others.
Now what is the best way to do this? capture the string into a text file using a BASH script and then read the file from the PHP page and print it in the webpage?
Neither of those languages would be my choice. PHP can read directly from the serial port, and skip all that crap with having the script open a file, write to it, close it, and then having PHP open it, read it, and close it.