The center said people in the Leeward Islands should monitor Bill's progress, though the core of the storm was expected to pass well to the northeast of the islands later today and early Thursday.
"The wind shear is light and the waters are warm," Todd Kimberlain, a forecaster at the center, said. "Those are two essential ingredients not just for the formation, but also the maintenance, of hurricanes."
Early this morning, Bill was centered about 460 miles east of the Leeward Islands and moving west-northwest near 16 mph.
The most significant threat could be to Bermuda, which the storm could pass in three or four days, Kimberlain said. But it also could move directly between Bermuda and the eastern coast of the U.S. without making landfall.
Either way, people near the coast can expect wave swells and rip currents in the next few days, Kimberlain said.
Forecasters had revised their Atlantic hurricane season predictions for this season after the first two months passed without any named storms developing.