Make sure that you do not get confused by Use popular search suggestions in the Firefox Search bar. The "Search Suggestions" are not your search history. The search suggestions are loaded in real time by querying the (Google) search engine site based on what you typed so far in the search bar. If "Clear Search History" is grayed out then the history is cleared or disabled.

You can disable the search suggestions by right-clicking the text field in the search bar and remove the mark before "Show Suggestions".

there is no "show suggestions" when right clicking text field

i tried that but it didn't work!