The 26-year-old from Okinawa ended the round level with compatriot Haru Nomura, Scotland's Catriona Matthew, England's Charley Hull and Americans Paula Creamer, Ashlan Ramsey and Alison Lee.
South Korea's Kwak Min-seo and American Jennifer Johnson opened with 69s while Swede Anna Nordqvist, American Brittany Licicome, Israel's Laetitia Beck and South Korean Kim Hyo-joo were among eight players bunched on 70.
American Michelle Wie and South Korean world number two Inbee Park, however, provided the most surprising headlines of the day.
Wie needed medical treatment on the 16th tee, her seventh hole of the round, after being stung by a bee in her right hand and she was never at her best as she struggled to an opening 76.
Park, the highest-ranked player in the field, fared even worse as struggled with a sore back on the way to a seven-over 80 before withdrawing from this event and also next week's Coates Golf Championship.
"I've always had a lower back problem and some weeks it just gets a bit worse," seven-times major winner Park told reporters. "Today happened to be one of those days."
Miyazato, in contrast, relished playing in the breezy conditions as she mixed six birdies with a lone bogey.
"Everything good for the first nine holes. I hit greens in regulation and made putts so after nine holes I was super excited," said Miyazato, a double winner on the LPGA of Japan Tour.
"Bahamas is always windy here but I like playing in the wind."
Creamer, a 10-time winner on the LPGA Tour who endured a difficult 2015 campaign while making changes to her swing and equipment, was delighted after a 68 that included an eagle and five birdies.
"Of course I would take this in a heartbeat," the 29-year-old said. "I have worked really hard. I'm really enjoying the game, I'm enjoying practising. I'm in a really good place and I hope I can keep it going."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine)
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