Used to have a solution to do this for Google search results via Google Sheets, but since the IP addresses that Google Sheets uses to make HTTP requests now seem to be either explicitly blacklisted or have been used to scrape Google so much by others that they're now hitting "please do a reCaptcha" errors, that solution is dead.

Anyway, you can do this for Bing where A1 contains some keyword you want to scrape:

=importXML("https://www.bing.com/search?q="&ENCODEURL(A1), "//*[@class='sb_count']")

It seems like there are some queries where Bing doesn't list the number of results at all, which throw an error, but other than that, this seems to work consistently.

Sir, I can do you a nice SEO.

Here's a better version that removes the " results" string and then casts the result to a number instead of a string:

=VALUE(substitute(importXML("https://www.bing.com/search?q="&ENCODEURL(B2), "//*[@class='sb_count']"), " results", ""))

Another wrapper function that replaces any "N/A" error messages (from results that don't show a result count) with a blank cell instead of an error:

=IFNA(VALUE(substitute(importXML("https://www.bing.com/search?q="&ENCODEURL(B2), "//*[@class='sb_count']"), " results", "")), "")

Sir, I can do you a nice SEO.