The oldest bowling club in the world still in existence was founded in 1299; a full 50 years before the first people settled in New Zealand.
The game has undergone various changes throughout the centuries. Bowls didn't even have a 'bias' until the 1300's and bowlers today would struggle to recognise the 'bowls' of the 14th century compared to those we play with now.

However, by the 19th century the game developed to a point where it is essentially the modern game that we know today.
It was in 1861 that the game first took root in New Zealand. This was courtesy of enthusiastic Scottish settlers and through founding the Auckland Bowling Club. This photo was taken circa 1862.

It is interesting to note that an older form of the game known as Crown Green Bowls, where the jack is biased and there are no set rinks, is still played in the British Isles today.