Most hosts will not allow outside connections to the MySQL server without authentication.
You will either need to provide them with the IP Address of your computer so they can set up an exception rule to allow your computer to access the mySQL Server, or set up a local testing server for development.
my personal preference is to use a local testing server for development, I find this he,lps speed up the development process.
See the learning resources page for details on setting up a local php testing server:
resources.php