Ryan Goins and Bo Schultz have been sent to triple-A to make room on the 25-man roster.
Bolsinger and Barnes will bolster a Blue Jays bullpen that has been taxed in two straight extra-innings losses to the Astros and Baltimore Orioles. The Blue Jays are in the midst of a 13-game stretch without an off day, which ends Aug. 11.
Acquired from the Los Angeles Dodgers at the trade deadline for Jesse Chavez, Bolsinger owns a 6.83 ERA and 1.518 WHIP in 27.2 innings at the major-league level this season.
Barnes, 26, has excelled at triple-A Buffalo since being recalled from double-A New Hampshire, having allowed only one run and five hits with 21 strikeouts and one walk in 17.2 innings. He was drafted by the Blue Jays in the 35th round of the 2010 MLB Draft.