What you need to do is set a cookie on the client's machine (that does not expire) when they click on the link to permanently bypass the splash screen.
So, on the page that the user gets to when they click the link to permanently bypass the spash screen, you would have code similar to the following, which will set the cookie onto the clients machine.
Then, on your spash screen page (at the top), you would have code similar to this, to redirect the user into the site if they have that skipSplash cookie set:
<cfcookie name="skipSplash" expires="never" value="1">
The 'skipSplash' cookie will remain on the user's computer indefinitely so that the next time they visit the site, the splash screen's page can read it and redirect them in.
<cfif isDefined( "cookie.skipSplash" )>
Hope that helps, and let me know if it works.