@Ask Harup Sejsbo Thanks for the question, On October 30, 2020, the Bing Search APIs moved from Azure AI services to Bing Search Services. Here is the document to Create a Bing Search resource through the Azure Marketplace.Here is the pricing and FAQ.
The Bing Custom Search API is an easy-to-use, ad-free search solution that enables users to build a search experience and query content on their specific website or across a hand-picked set of websites or domains.
[http://customsearch.ai]
Create an instance
Define the custom index
Adjust ranking
Test
Deploy