You Do Need power plug adapter while traveling from New Zealand to Bahamas.

Here is Why You Need An Adapter

The outlet and plug type used in Bahamas are A and B and in New Zealand is I. This is how they look like.

New Zealand

In New Zealand, outlets of type I are in use.

Type I

Bahamas

In Bahamas, outlets of type A and B are in use.

Type A

Type B