I would like to write a program that will find bus stop times and update my personal webpage accordingly.
If I were to do this manually I would
That site doesnt offer an API for you to be able to get the appropriate data that you need. In that case you'll need to parse the actual HTML page returned by, for example, a CURL request .
As long as the layout of the web page your trying to 'scrape' doesnt regularly change, you should be able to parse the html with any modern day programming language.