I believe you are referring to using the Bing custom search API for image results. I have tried this experience with the custom search UI, and it is able to fetch web and image results from the website I have allowed in my configuration. See screen shot below:
I have tried this scenario with multiple websites, and it works to pull images of that website. If you do not see any results, then the images of the website are most probably not indexed by Bing. Also, ensure you don't add a search engine website in your active list, as adding search engine websites will not provide the image search results seen from the actual search website i.e. for example, adding bing.com will not help in this case.
While using the API programmatically, the custom config id needs to be provided as a param as mentioned in this sample. With hosted UI experience, you also need to enable image search in the advanced setting configuration. I hope this helps!!
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