Bryant was starting the tour Tuesday in Port Angeles and will end it in Seattle on Aug. 2, the day of the state’s primary election.
Other cities he’ll visit include Bellingham, Walla Walla, Auburn and Moses Lake.
Bryant, previously served on the Seattle Port Commission since 2008, says the state needs new leadership. Inslee, who was elected in 2012, is seeking a second term.
An April poll by independent pollster Stuart Elway found 48 percent of voters surveyed preferred Inslee while 36 percent supported Bryant. Another 16 percent were undecided.
Inslee has raised more than $7 million in his re-election bid, compared to the $2.3 million raised so far by Bryant.