How to delete specific website search history from Bing ?

You cannot delete search history of an specific website from Bing. You can delete history of a site from your web browser only. However, you can delete your complete search history from Bing.

Here are the steps to clear search history form Bing search engine.

1. Firstly, you need to visit - bing.com.

2. Then, goto settings->Go to Search History.

3. Here, you will see "Clear All" button, click on this button and it will clear your complete search history from the Bing.

4. You can also turn off this feature from the same page.

You can just open your browser from which you wants to remove the history of the specific website then press CTRL+H to open up the history page. Then you can select the specific website to remove the browsing history. And then you need to press to the button to "Clear the browsing history". Now its all done for the process to remove the browsing history of a specific website.

It is not the search engine, from where you should try to delete your history. It is te browser which you are using from where you need to delete them. For example, if you are using Google Chrome, or Internet Explorer, Firefox etc, the option for deleting the history would vary in their settings.
In Google Chrome, you get a settings button right beside your address bar. There in the history tab, you get two options-
1. clear browsing data
2. Remove selected items

So once you check on the sites you want to remove and click on "remove" they will be removed.
But make sure you also delete temporary internet files, cookies and caches to delete them permanently.
But i don't think, Internet Explorer offers you to delete particular sites.