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

Here is Why You Need An Adapter

The outlet and plug type used in Turkmenistan are C and F 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

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F