An Elizabethan expression meaning "old news", or "No shit, Sherlock". Hamlet says this contemptuously to Polonius in Hamlet, Act Two, Scene Two. Here's how the scene goes in the Oxford Shakespeare, the best version out there:
Polonius: The actors are come hither, my lord.
Hamlet: Buzz, buzz.
Polonius: Upon my honour--
The version noded on this site gives some different spellings:
LORD POLONIUS The actors are come hither, my lord.
HAMLET Buz, buz!
LORD POLONIUS Upon mine honour,-
What's the deal? There are three versions of Hamlet: The bad Quarto (Q1), the good Quarto (Q2), and the First Folio. "My" and "mine" are used interchangeably between them, so the Oxford Shakespeare always goes with the more modern "my" before words with vowels: Why err on the side of anachronism? More important to the topic at hand: "Buzz, buzz" is made up. In the various texts, Hamlet's line is never spelled that way. See for yourself:
The First Quarto: (The VERY BAD version)
Cor. The Actors are come hither, my lord.
Ham. Buz, buz.
Cor. The best Actors in Christendome,....
The Second Quarto:
Pol. The Actors are come hether my Lord.
Ham. Buz, buz.
Pol. Vppon my honor.
The First Folio:
Pol. The Actors are come hither my Lord.
Ham. Buzze, buzze.
Pol. Vpon mine Honor.
Editing styles, of course, are often taste as much as science. So let's settle the matter through an appeal to authority. Let's have frigging James Joyce solve the issue for us. Open up your copy of Ulysses to the Scylla and Charybdis episode, which is soaking wet with Shakespeare. And please, let's bypass all discussion of which version of Ulysses is more correct. We're in too deep already. They all agree that Stephen thinks about the money he owes to AE (George Russell):
I paid my way. I paid my way.
Steady on. He's from beyant Boyne water. The northeast corner. You owe it.
Wait. Five months. Molecules all change. I am other I now. Other I got pound.
Buzz. Buzz.
But I, entelechy, form of forms, am I by memory because under everchanging forms.
I that sinned and prayed and fasted.
(Emphasis mine). If "buzz" is good enough for Joyce, it's good enough for me. Let's stick with "Buzz".
Buzz, Buzz.