Ask.com search bar pops up all the time in Safari

It sounds like an unauthorized extension. Go to Safari Preferences > Extensions tab: --you can disable any extensions you don't want by selecting it, and un-checkmarking the box. You can also delete it completely by clicking on the Uninstall button on the righthand side window.

Here's a couple of support articles for more information:

https://support.apple.com/guide/safari/get-extensions-sfri32508/mac

https://help.ask.com/hc/en-us/articles/360001679593-How-do-I-uninstall-the-Ask-Toolbar-or-Search-App-from-Safari-in-Mac-OS-X-