What is origin of the phrase "Don't say boo" or "Didn't hear boo"?

Saying bo [or boo] to a goose

Eric Partridge, A Dictionary of Slang and Unconventional English, second edition (1937) has this entry relevant to expressions involving "saying boo":

bo or boo to a goose, say or cry ; occ. to a battledore. To open one's mouth ; to talk, speak : gen[erally] in negative. Coll[oquial] from ca. 1580.

Various searches at Early English Books Online related to "saying bo [or boo] to a goose" turn up a number of matches from as early as William Watson, A Decacordon of Ten Quodlibeticall Questions Concerning Religion and State (1602); unfortunately, I have not been able to find the relevant goose-bo[o]ing excerpt from that treatise in a snippet-view search of the text at Google Books. Still, a number of relevant matches do turn up, starting with two from 1606.

From Barnabe Rich, Faultes Faults, and Nothing Else but Faultes (1606):

The reliques of the Beadles whippe (me thinks are vnfit to bee made Souldiors; but our Souldiors in these dayes, are become protested enemies to all sorts of Poultrie, as Capons, Hens, Chickens; nay, they will not spare the Cocke himselfe, if hee come in their walke. But if they meete a flocke of Geese, it shall neuer bee said when they are gone, but that they durst say, Bo to a Goose.

From Thomas Dekker, The Seuen Deadly Sinnes of London Drawne in Seuen Seuerall Coaches ... (1606):

It was excellent musicke (considering how many dis∣cords there were) to heare how euery particular regiment in Pouerties Camp, threatned to plague the Gold-finches of the Cittie, and to pluck their feathers, if euer they made a breach. Taylors swore to tickle the Mercers, & measure out their Sattins & velvets without a yard before their faces, when the prowdest of them all should not dare to say Bo to a Taylors Goose.

From Thomas Middleton, A Chast Mayd in Cheape-Side (ca. 1613):

Porter. If I see your Worship at Goose Faire, I haue a Dish of Birds for you.

Yellow-hammer. Why dost dwell at Bow?

Porter. All my life time Sir I could euer say Bo, to a Goose. Farewell to your Worship.

From I.H., The House of Correction: or, Certayne Satyricall Epigrams (1619):

An Archer, bragging, sayd, he well did know / How to bring any man vnto his bow: / Yet, when he put his knowledge into vse, / Hee hardly could say Bo vnto a Goose.

From John Taylor, A Iuniper Lecture With the Description of All Sorts of Women, Good, and Bad (1639):

Out you Slabber Choppes, goe trudge with thy fellow Hob, and drive the Cart; Thou art a course Clown, a meere Coridon, thou art not able at any time to say boo to a Goose, un∣lesse it be to a bowle of pottage that holds a Gallon; and a Barly bagge pudding of a yard long, and some Bull Beefe, there I confesse thou wilt, and canst shew thy selfe a man: ...

Taylor's example is noteworthy for being the earliest instance I could find in which the thing said was "boo" rather than "bo."

And from Thomas White, "Mr. Blacklow's Reply to Dr. Layburn's Pamphlet Against Him" (1660):

I read farther, how for executing this command of my Lords Mr. Bl. was so incensed against him, that he cry'd him down in divers companies, and the ordinary character he gave him was, that he was an illiterate man not able to say Bo to a Goose. Mr. Bl. reply'd that the Doctor cared not how unlikely his tales were, so he said somewhat that might passe amongst those, who knew no more of the businesse than they found in his paper; ...

Saying bo to a goose follows from a more general circumstance of saying bo. A search for the more generalized expression turns up instances from as early as 1526. From Walter Smith, XII. Mery Iests, of the Wyddow Edyth (1526/1573):

What yf we be punished with our owne rod? / Whom shall we erecte the fault vnto? / But to our selfes that can neuer say bo:

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Saying boo without a goose in sight

Examples of "saying boo" in the sense of "saying something [or anything]" without an accompanying goose are fairly common in U.S. newspapers from 1836 onward. Here are some early examples.

From "A Change of Mind," in the Crawfordsville [Indiana] Record (February 20, 1836), reprinted from the Cincinnati [Ohio] Mirror:

And so she went on, cutting right and left, and ridiculing her brother's notion that a kind temper was as good a thing as a keen intellect; 'she'd rather be a very vixen,' which Bill muttered she was already, 'than a good, quiet, soft, soapy piece of amiable stupidity, that daresn't say boo, lest people should think it ill-natured.'

From a letter to the editor of the Constantine [Michigan] Republican (August 16, 1837):

The whigs themselves here do no know, or hardly ever heard of the man nominated for them to support, (Mr. Wells.) To be sure they know he was a member of the Convention to form the constitution, but he never said "boo" all the time he was there. A pretty man that, to send to Congress from the state of Michigan.

From "Nettle Bottom Ball," in the Ottawa [Illinois] Free Trader (May 30, 1845), reprinted from the St. Louis [Missouri] Reveille:

Talk about gracefulness, did you ever see a maple saplin' movin' with a south wind?—It warn't a crooked stick to compar' to her to her, but her old dad was awful. He could jest lick anythin' that said boo, in them diggins, out-swar satan, and was cross as a she bar, with cubs.

From "Jedediah Parsley's New-Year's Parin' Bee," in the Richmond [Indiana] Palladium (March 17, 1846):

Howsever they rubbed her all over wherever the sider went, and may I be twisted intu a pigtail, if in half a hour she didn't look as Jim Spooner sed, like a whited sepulchre only wusser. Her frock was sort of pinkish, and wherever the perlusion went it took out all the sider culler, and that was jest no culler atol. I guess she remembered the dandy as long as she did poor Joe Spraig, who slunk into a corner and never said boo the rest of the evenin'.

From "How Paddy Casey Got in the Calaboose," in the [Hawaii] Polynesian (July 8, 1848), reprinted from the New Orleans [Louisiana] Mercury:

Paddy—'I am for Claiborne to the last, an' against Lewis for iver.'

Judy—'Bad manners to me, but 'ti jist like you—'its you always had the bad taste. You for a Clay burn are you now; troth I wish you wur, an' in it took. Thin I'll stick to Shoeless for iver, and I wud like to hear the man that wud say boo against him.'

From "Only Half Married," in the Pontiac [Michigan] Gazette (February 7, 1852):

B[ride]. ‘La! John, there's no use of being in such a hurry.’

G[room].—‘Now Sary, don’t say boo! till it’s over; let ’em drive. Go at it Squire—hurry up the cakes—moderate, but don’t splurge—slow, hut alfired sartain. Wake snakes—won’t Bets Bradford howl when she hears that I'm married.

From "Mollie Pickwood," in the Pontiac [Michigan] Gazette (April 1, 1854):

"Ain't I going to be married for the sake of having my own way? I shall race, chase, romp, and nobody shall say boo! to me after I'm married."

The fuller "boo to a goose" was not lost at this period, however, as we see in this example from "A Little of Every Thing," in the Boston [Massachusetts] Pilot (February 21, 1846), reprinted from the Advertiser:

An attacheé to one of the Departments was following the lead of Mr. Allen, Mr. Cass, and others, by boasting of our superiority to England in military prowess, and the probability ol vanquishing her in case of war. One of the company ridiculed his vaunting fit and said, “ Why, as for yourself, G, you wouldn’t dare ‘to say boo to a goose!'” “I don’t know as to that,” was the reply, “but I went up to the Secretary of State today and said Bu-chanan!

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Conclusions

Expressions of the form "say boo" (or "say bo") go back almost 500 years. The most popular early form of the expression seems to have been a taunt along the lines of "wouldn't say bo[o] to a goose." The expression (usually without the goose) continues to be common in the United States, where it continues to mean much the same thing that it did in the early 1600s. Perhaps the most surprising thing about "saying boo" is that, despite its long record in English, it remains colloquial or at least informal.