You Do Need power plug adapter while traveling from Bermuda to Fiji.

Here is Why You Need An Adapter

The outlet and plug type used in Fiji is I and in Bermuda are A and B. This is how they look like.

Bermuda

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

Type A

Type B

Fiji

In Fiji, outlets of type I are in use.

Type I