Bivens appeared out of the bullpen in Thursday's 3-0 loss to the Brewers, giving up two runs on two hits and no walks while striking out two in two innings.
Bivens did not factor into the decision in Sunday's win over the Padres, allowing one run on four hits and a walk while striking out three over 4.1 innings.
The Giants recalled Bivens from Triple-A Sacramento on Thursday, Maria I. Guardado of MLB.com reports.
The Giants optioned Bivens to Double-A Richmond on Tuesday, Shayna Rubin of the San Francisco Chronicle reports.
San Francisco recalled Bivens from Triple-A Sacramento on Saturday.
The Giants optioned Bivens to Triple-A Sacramento on Saturday.
Bivens is expected to serve as a bulk reliever behind opening pitcher Erik Miller in Friday's game against the Guardians, Shayna Rubin of the San Francisco Chronicle reports.
Bivins will start Sunday's game against the Dodgers, Susan Slusser of the San Francisco Chronicle reports.
Bivens (1-1) took the loss Wednesday as the Giants were downed 6-5 by the Cubs, giving up three runs (two earned) on five hits and two walks over two-plus innings. He struck out one.