There are a few ways this could be done.
The simpliest way would be to set the source or PageLink of the PageSearch control (assuming this is the standard search template) to the homepage of your site. This would limit the search to items under the homepage (automatically excluding the recycle bin as this sits outside the website).
Another way would be to add a filter to the PageSearch by wiring up to the filter event and then removing pages from the search results if they are a descendant of the recycle bin page (There is a reference to the recycle bin in the Configuration class Configuration.Wastebasket). I believe there is a code sample on this site or in the SDK.
Cheers,
Jeremy