Errors connecting to MySQL database from alternate domain

I have two domains on two separate servers, foo.com and bar.com.

I have a website and MySQL database setup on foo that I want to migrate to bar, but bar doesn't have MySQL.

As a solution, I'm moving all the files across but leaving the database on foo, and connecting to it remotely.

I'm currently connecting like so:

connect.php

$hostname = 'database.foo.com';
$username = 'username';
$password = 'password';
$dbname   = 'database';

try {
    $dbh = new PDO("mysql:host=$hostname;dbname=$dbname", $username, $password);
}

catch(PDOException $e){
    echo($e->getMessage());
}

This works fine on foo.com but when I migrate this file to bar.com I get this error:

SQLSTATE[HY000] [2003] Can't connect to MySQL server on 'database.foo.com' (110)

I can have the two sites, foo.com and bar.com open in two windows, and one will work while the other doesn't - despite the fact that they are both connecting (or trying to connect) to the same database.

Why is this happening and how can this be rectified?

via Chebli Mohamed