I don't know of this has come up before. If so, bad luck:-)
Those foreign to English often pronounce this word differently than I, and it got me wondering about whether I'm really saying it correctly. At dictionary.com I found some interesting notes on this one: http://www.dictionary.com/search?q=bury
And that pretty much answered half my question.
It seems bury is generally spoken exactly the same as 'berry', or rather it rhymes with it as the link questions; 'Why does bury rhyme with berry?' it asks. It states how in certain parts of England bury was/is pronounced biry, boory (like jury) and bery. Fair enough, nothing uncommon. English students often opt for a pronunciation more like one of those rough, prickly husks, a burr, with a 'y' on the end though - and why not? One might agree that at least some would pronounce the 'bury' in Canterbury as such, as long as the '-bury' part is not swallowed as '-bry'. Or would you exclusively go for something like canterbery or cantabery?
Am I making myself clear? - Probably not.


p.s. How do you lot pronounce library, btw?
... ducking for cover [g]