The National Hurricane Center said the Leeward Islands should monitor Bill's progress, although the core of the storm was expected to pass northeast of the islands late Wednesday and early Thursday.
"The wind sheer is light and the waters are warm," said Todd Kimberlain, a forecaster at the center. "Those are two essential ingredients not just for the formation, but also the maintenance, of hurricanes."
Early Wednesday, Bill was centered 460 miles east of the Leeward Islands, moving west-northwest at 16 mph.
Bermuda faces the most significant threat when the storm passes by in three or four days, Kimberlain said. But the hurricane also could move between Bermuda and the eastern coast of the USA without making landfall.
Either way, people along the eastern coast of the USA can expect wave swells and rip currents in the next few days, Kimberlain said.
Meanwhile, people in flood-prone Haiti and the Dominican Republic were relieved when Ana, the first named storm of the Atlantic season, largely spared their shared island of Hispaniola.
The two Caribbean nations are vulnerable to storms, with many impoverished people clustered along rivers, but there were no reports of major damage from the remnants of Tropical Storm Ana.