Nobody can see your connection string if they look at the source, it can only be seen by looking at your raw code. I would also have it inside a separate file, and include the file on your page. This also helps if you need to change the password, as you won't have to edit every page that uses a connection - you'll only need to edit the one file.
Alternatively, you can have a connection string in an include file and place it outside of document root. This stops people getting to this file using a browser or if they attack your FTP. This will help security of your plain-text passwords, but is still accessible if somebody gets/has access to your local directories. To do this, you may need to configure a PHP configuration variable, open_basedir, which allows your script to talk to a file outside of root. This all depends on if you have access to a folder behind root of course, and if you can change that configuration variable.
Other than that, there's not much that can be done.
Include File Example:
Create a file called conn.php and store your connection in there.
$dbConn = mysql_connect($host, $user, $pass);
mysql_select_db("dbName", $dbConn);
On the page that needs the connection, include the conn.php file like so:
<?php
include("conn.php");
if (!dbConn) {
die('Sorry, our database did not load. Please try again later.');
exit();
}
$result = mysql_query("...");
?>