The Blue Jays will also receive a player to be named later.
The 34-year-old Bass, a right-hander who is 2-3 this season, is having a breakout year, pitching to a 1.41 ERA in 44 2/3 innings. He has struck out 45 and walked just 10.
Pop, 25, is 2-0 with a 3.60 ERA in 20 innings pitched. The Blue Jays drafted the right-hander in the 23rd round of the 2014 draft, but he played collegiately at the University of Kentucky and went back into the draft in 2017.
The Marlins are receiving Jordan Groshans, the Blue Jays' first-round pick in the 2018 draft. The 22-year-old shortstop currently is playing for Triple-A Buffalo and has a .247 average with a home run and 24 RBIs at two levels of the Blue Jays' minor league system.
Toronto (57-45) currently sits atop the AL's wild-card standings.