The 33-year-old, a twice winner on the PGA Tour, went on to shoot a second successive three-over-par 74 at the TPC Scottsdale to miss the cut at the Phoenix Open by seven strokes.
After consulting with PGA Tour officials for more than an hour, Bowditch released a statement: "I would like to apologise to my family, friends and supporters, as well as the PGA Tour and Waste Management Phoenix Open for the incident reported today.
"As I intend to fully cooperate with the authorities, I will not be making further comment at this stage."
According to the Scottsdale Police Department, Bowditch was found asleep in a white pickup truck after a motorist reported that a vehicle had been swerving all over the road in the early hours of Friday morning.
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The truck, a courtesy car provided by the tournament, was located with its engine running after remaining stationary through two green traffic signals.
The driver, identified as Bowditch, was woken by a traffic officer and later arrested with a blood alcohol content over 0.20 percent, Scottsdale police said.
In Arizona, drivers with a blood alcohol concentration of 0.08 percent are considered to be driving under the influence of alcohol.
(Reporting by Mark Lamport-Stokes in St. Augustine, Florida; Editing by Nick Mulvenney)
