Every search done this way will also be piped only through its recently released Edge browser.
In a blogpost, Microsoft said it was making people use Bing so they could get the most out of other search-related features in its products.
Many Cortana users have previously preferred to carry out searches with Google rather than Bing.
Windows users will still be able to install other web browsers and use other search engines outside Cortana, said Ryan Gavin, Microsoft's head of search and Cortana, in the blogpost.
However, he said, Microsoft was adding extras to Edge and Bing that meant it made sense to tie these programs to Cortana instead of other search engines and browsers.
Anything else would be a "compromised experience that is less reliable and predictable", he said.
The extra features will differ depending on what people search for, but if someone used Cortana to look for a restaurant the browser would take them to the relevant webpage and add in a map to show the closest locations, Mr Gavin said.
On technical queries, these extras would return the usual list of potentially helpful pages but would return videos and other explainers, adding detail.
Mr Gavin said Microsoft was investing in these "end-to-end personal search experiences" and hoped they would prompt a series of actions after users carried out one search.
As an example of this, Mr Gavin said a future search for "tickets to a Rihanna show" would open up search results for seats tied to a user's preferences and complete every part of the buying process apart from the final click on the payment button.
Writing on the Search Engine Land news site, analyst Danny Sullivan said it was a mistake to limit "deliberate choices" users made.
"I think Microsoft is taking some big liberties here," he said.
Mr Sullivan went on to criticise the convoluted process Windows 10 users have to follow to change the default search engine used on Edge and Internet Explorer.
Although Microsoft has had some success getting people to use the Bing search engine, Google still dominates in this market.
Statistics gathered by Statcounter suggest that globally more than 90% of searches are carried out via Google. By contrast, Bing accounts for about 3% of searches.
Microsoft is forcing people to use its Bing search engine with the Cortana digital assistant in Windows 10.