"She's doing good [now]," Bartlett said. "They gave her some medicine to try and calm her down. She's still having contractions. Hopefully the medicine will kick in a little more."
The couple is expecting their first child, a boy, on July 6.
"He kind of wants to come out now," Bartlett said.
Kelly is back at the couple's St. Petersburg home with her mother, whom they flew in from New York.
"Obviously, it's our first time, and we don't know what everything means right now," Bartlett said. "With her contractions, we went crazy. With her mom in town, she's helping to explain everything."
Bartlett, who is hitting .237 with no home runs and eight RBIs on the season, was back in the lineup for Friday night's game against the Cardinals, albeit in an unfamiliar spot. Since the Rays were playing in a National League park, the DH is not in effect, so pitcher Andy Sonnanstine was in the ninth spot.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.