Bing has started showing a "Search within xyz.com" bar for some searches. This appears in the organic listings and not ads (like Google has).

This has recently started showing for one of my clients but lands on the wrong page internally when used. I've searched for instructions on how to control this but to no avail.
How can we make sure users end up landing on a page of results for the search terms entered into this box?
How can we get this to appear for other clients' sites?