"The command wasn't all the way there, but the strength and everything else felt really good," said Bassitt, who has been sidelined by shoulder soreness.
The A's will wait to see how Bassitt feels Tuesday before determining his next step. The ultimate goal is to have him start another game before season's end.
"I want to continue to prove not only that I'm 100 percent back and there's nothing wrong," Bassitt said, "but just continue to build upon what I've done this year."
Bassitt, who called it "bittersweet" being back in Chicago, began the season in the A's bullpen but struggled with command and was sent to Triple-Nashville, before returning to Oakland in June as a starter. He excelled in that role during three separate stints with the big league club, pitching to a 2.73 ERA despite a 1-6 record across 10 starts.
"Based on injury, we've gotten to take a longer look at him and he's really been good," A's manager Bob Melvin said. "Less maybe one or two outings, he's kept us in every game. We've given him barely any run support, but you can see him getting more and more comfortable each time going out there starting.
"He's got the tenacity to him. He wants to be out there when the game's on the line, and it's been really nice to see. We really feel like we have a guy that's going to be with us for a while and has quite the upside."
• Outfielder Billy Burns went through a full range of baseball activities in Chicago on Monday, though the A's don't plan on rushing the speedster back into game action.
"I'm not even sure he would be available tomorrow," said Melvin, who hinted Burns could potentially miss the entire four-game series.
"When you're dealing with a hamstring for a guy that uses his legs as much as he does, we don't want to have this happen again, because it would probably cost him the rest of the season," he said. "We will be careful with him."
• Right-hander Edward Mujica, who sustained a right hamstring strain during Sunday's loss in Arlington, is "going to be a little while," according to Melvin. Mujica is expected to stay away from baseball activity for several days.
• Catcher Stephen Vogt, who is still experiencing pain in the groin area after taking a foul tip last week, has yet to resume baseball activity.