The storm peaked on Friday as a Category 4 hurricane with winds of 140 miles per hour (220 kph).
The NHC said, with maximum sustained winds of 120 miles per hour, Bud is now moving northwest at about seven miles per hour.
The hurricane is moving north-west at about 10mph - a course it is expected to take until mid-week, the NHC said.
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Some additional strengthening is possible today but a slow weakening should begin tomorrow. Rainfall of 3 to 6 inches (75 to 150 millimeters), with isolated patches of 10 inches (250 millimeters), was possible into Tuesday afternoon. "These rains could cause life-threatening flash floods and mudslides", the agency warned.
A tropical storm watch is in effect between Manzanillo, Colima, and Cabo Corrientes.
Having another potential storm develop so soon is not unusual, hurricane center spokesman Dennis Feltgen said, even if it seems stormier than usual in Florida.
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"Swells generated by Bud will continue to affect portions of the coast of southwestern Mexico during the next few days", the NHC said.
The Weather Channel reported that the hurricane could prompt a "surge of moisture" in the southwest United States, which would lead to an increase in rain showers and storms.
Both Alberto and this system popped in the southern Caribbean, where warm waters early in the season can help fuel tropical cyclones while waters remain too cool farther east in the Atlantic.
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The Atlantic hurricane season lasts until November 30. The depression is now located about 665 miles southwest of the southern tip of Baja California with maximum sustained winds of 35 miles per hour.