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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Martin are C and E 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

Saint Martin

In Saint Martin, outlets of type C and E are in use.

Type C

Type E