The word bury is pronounced ˈberi. There is also a place called Bury and that has the same pronunciation. However, as a place-name ending the pronunciation is bəri or more often bri. Here are a few examples:
Adderbury Daresbury Norbury Salisbury (= ˈsɔːlzbri)
With thanks to Alex Rotatori and Graham Pointon for a correction.