Hi,
Does the issue occur before or it is the first time to use Cortana for searching?
What's your system build? Please run "winver" to check the details number.
We have a little confuse with your existing issue, so 2 scenarios below are assumed.
"I can't even get it to open google"
If you want to use Cortana search result show in Google engine instead of bing, I am afraid it would be not available unless with some third party software or extension as Cortana's cloud-based brains are powered by Bing.
"windows update made cortana stop using bing"
If your Cortana can't even search with bing, we could check if it works on a new created user account. Or we could register with the following command line in PowerShell. (Please run command as administrator.)
Get-AppxPackage -AllUsers Microsoft.Windows.Cortana | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}
If we have misunderstood about your issue, please reply to us directly.
Bests,