The storm's maximum sustained winds decreased to near 65 mph (100 kph) early Tuesday with gradual weakening expected over the next two days.
The U.S. National Hurricane Center says Bertha is forecast to pass midway between the East Coast and Bermuda later in the morning.
The storm is centered about 475 miles (765 kilometers) west of Bermuda and is moving north-northeast near 22 mph (35 kph).
On Sunday, the storm buffeted parts of the Bahamas and the Turks & Caicos with rain and gusty winds, after passing over the Dominican Republic. Earlier, it dumped rain on Puerto Rico.