Could you check on their results page for a link similar to:

• Opt out
• Why do I get this page
• etc.

That may lead to a page similar to the following which turns off that feature (this is an old link and might not be current):

http://webhelper.centurylink.com/prefs.php

Thanks but I have tried that 10 times and the opt out (disable) does not make it stop.

I just re-read your original question: I read it as "the address bar" but if you are using a different bar, then the following answer may be irrelevant.

I assume this problem occurs only with one word searches in the address bar.

If it occurs with ALL searches, you may need to:

(1) Change your default search engine. Please see this article: Change your default search settings in Firefox, and/or

(2) Remove a bad extension. One possible culprit would be an extension. You can view, disable, and often remove unwanted or unknown extensions on the Add-ons page. Either:

• Ctrl+Shift+a (Mac: Command+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then cast a critical eye over the list on the right side. All extensions are optional. If in doubt, disable or remove.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

If only one-word searches are affected:

By default, Firefox should be submitting those to your default search engine first before checking whether they are valid addresses. Could you check on whether that setting has been switched? Here's how:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful.

(2) In the search box above the list, type or paste keyw and pause while the list is filtered

(3) If the keyword.enabled preference is bolded and "user set" to false, double-click it to restore the default value of true

(4) In the search box above the list, type or paste fix and pause while the list is filtered

(5) If the browser.fixup.dns_first_for_single_words preference is bolded and "user set" to true, double-click it to restore the default value of false

If you changed either of those settings, please test again. Any improvement?