"Significantly cooler waters around the southern tip of Baja California should reduce Bud's intensity below hurricane status before it reaches that land", the centre said.
Forecasters said Bud was expected to strengthen further before a slow weakening trend starts Tuesday.
In the Atlantic basin, the hurricane center said there's a 20% chance that a tropical depression or storm will spin up witin the next five days in the Caribbean or the Gulf of Mexico. This media house does not correct any spelling or grammatical error within press releases and commentaries.
Bud was moving toward the north-northwest at about 6 miles per hour (9 kph) and was forecast to approach Baja California Sur on Thursday as a tropical storm.
Swells from Bud "are likely to cause life-threatening surf and rip current conditions" along the west coast of Mexico, according to the hurricane center.
By mid-morning on Tuesday, Bud was moving towards the northwest at around 6 mph (9 km/h) and was around 325 miles (523 kilometers) south-southeast of Cabo San Lucas.
The 2015 season began with Category 4 Hurricane Andres followed by Category 4 Hurricane Blanca, the record-earliest-in-season second eastern Pacific hurricane and major hurricane, which later became the record-earliest Baja California landfall, as a tropical storm.
The Weather Channel said predicted it would be a tropical storm when it arrives in Baja California Sur.
The outer bands of Bud will bring heavy rain to western coast of Mexico today, some areas could see up to 10 inches.
The National Weather Service's seven-day rainfall forecast.
"Bud" ramped up to a Category 3 hurricane.