A "Americanism" or an American expression used in the 19th century. Originally used in the converse sense: "Tell the president what you think 'with the bark on,'" which refers to words in their natural, unpolished state, such as unfinished wood that still has it's bark covering it, or "Plain (informal) Language. Using the colloquialism "words with the bark off" should mean "words that have been refined" or "polished" in some way, so your sentence may also read: "Don’t accept the post unless you are free to tell the President what you think “using formal language.” However; the "feeling" of your uncommon phraseology denotes the opposite. Use of "unless you are free to..." may change the intent of "with the bark off" idiom, since most people would speak with a government leader using formal language to begin with. In your example, the writer may likely mean: Don’t accept the post unless you are free to tell the President what you think “in plain language," without flowery language. Plain Talk. Straight Talk. In any event, this is an old saying that is not used much anymore.