Firefox is designed to allow you to pick your default search engine and have it remain unchanged (at least until a new company sign up with Mozilla as the default search provider, but that doesn't happen very often).

Does the problem search engine show up as "Bing" or "Bing Search Engine"? The "Bing" is built in; the other one appears to be malware. See: Firefox will not stop changing search provider from Google to "Bing Search Engine" (Not standard "Bing"!)

Try to rename/remove search.json.mozlz4 (and possible search.json, search-metadata.json, search.sqlite) in the Firefox profile folder with Firefox closed to rebuild the search engines registry.

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

Firefox will rebuild the search.json.mozlz4 file from the builtin search engines.

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration is causing the problem.

• switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Appearance
• do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

See also:

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware