It seems plausible this idiom comes from hunting.
According to Idiomation, back in medieval times, noblemen hired others for the purpose of flushing animals out from the brush. Apparently, this was done by making lots of noise, which they did by either shouting a whole bunch, or perhaps by whacking the bushes with a stick. This was all for the sake of scaring the animals out from cover, making them easier targets for the hunter.
The creatures emerging from the brush were not limited to cute squirrels and small birds. Sometimes, it was something far more dangerous, like a wild boar with sharp tusks. You wouldn't want your legs anywhere near such beasts, so wisely, the men would solve this problem by hanging back and beating around the bush, giving themselves enough space to react if necessary.
Thus, the men were avoiding their main target: the bush, instead choosing to keep their distance from it.
To go along with the story above, there are poems written from the 15th and 16th centuries that talk about beating bushes and birds being caught as a result. For example, a poem written in 1572 by George Gascoigne, reads:
"To thinke bowe he abused was, alas my heart it bleedes:
He bet about the bushe, whiles other caught the birds …"
Note: Finding the origins for phrases can be very difficult a lot of the time, as it's hard to find that one person or even area where an idiom started.
For the most part, what's given are possibilities in how a phrase could have originated, but not necessarily how it actually did. Additionally, early recorded forms of a saying will be given, and these tend to come from old books, newspapers, poems, or plays.
However, if phrases are being printed in forms of media, like a newspaper, that's usually a sign to show it's already a well known saying, and is probably much older.
Ultimately, you get an approximate on how long a phrase has been used for, and gain a little understanding on where a phrase's roots are from.
Know Your Phrase has lists of idiom meanings, and more are being added!
* Alex refused to tell me what really happened to those chocolate chip cookies that Monday morning, all he did was beat around the bush when I asked him directly.
* This is a waste of time, either quit beating around the bush and tell me what your complaint is, or get back to work!
