IIRC it depends how the ads are routed. The ads could be piped through duckduckgo so Bing only receives searches to return contextual ads for but has no knowledge of the IPs for each search. Duckduckgo then embeds the ads in the search page and returns it to the searcher, then forgets their IP.
On the other hand if there's just a bit of javascript on the search page that says "Tell bing to put ads on this page using the search bar text" then bing would be able to link the search to an IP and you lose your privacy.