Smith, acquired by the Mariners in an offseason trade that sent catcher Mike Zunino to the Tampa Bay Rays, is hitting .165 with two triples, one homer, five RBIs and eight stolen bases in 27 games this season.
The 25-year-old outfielder had a breakout season in 2018 for Tampa Bay, hitting .296 and tying for the American League with 10 triples. He also had two homers and stole 40 bases.
Bishop, 25, made the Mariners' Opening Day roster and went hitless in one at-bat before being optioned to Triple-A on March 23. He was hitting .267 with three homers and 13 RBIs in Tacoma.