Bay arrived at Citi Field on Friday prepared to ride a stationary bicycle.
He hopes to return to game action before the season ends.
"I expect to. But, at the same time ... I haven't done anything in a month and there's a certain rigor of programs you need to go through," Bay said. "I'm also fighting not just getting back into shape, but also making sure my head doesn't hurt, either. You're going against two things.
"I fully expect to and I want to [return]. I also understand we have time constraints as well. If the consolation to all of it is going into the offseason knowing I didn't have any restrictions, that's definitely something that I need to do."
Bay said persistent headaches began to subside a week ago, except for certain brief points during the day. He was cleared by Mets doctors to begin physical activity when he went 48 hours without suffering any concussion-related symptoms.
Bay said he had not knowingly had any previous concussions that might have contributed to these symptoms lasting nearly five weeks. His brain injury occurred when he suffered whiplash while catching a fly ball at Dodger Stadium on July 23. Bay also played the next two games, but felt uncomfortable after the series finale against the Dodgers and on the cross-country flight back to New York.
Bay consulted Minnesota Twins first baseman Justin Morneau, who also is dealing with concussion issues.
"That night I felt like I ran into a wall, obviously," Bay said. "And the next day, honestly, I was sore body-wise, but I didn't feel anything. It's kind of hard to try to fault anybody when you don't say anything and when you have nothing wrong. For whatever reason, the next day -- I don't know if something triggered it or just that [it] was the delay. No one has an idea. But not one of the symptoms presented itself [right away]."
Even if Bay returns for the final week or more of the season, his first year in New York will have been underwhelming after signing a four-year, $66 million deal. He is hitting .259 with six homers and 47 RBIs in 348 at-bats.
"You can't sugarcoat it -- not good," Bay said about his first season as a Met. "I'm definitely a lot better than that. Like I've said before, this is the reality. This is what happened. Unfortunately it didn't go as expected. But I have plenty of time for redemption. For whatever reason -- everybody can speculate on whatever the reason might be -- I just chalk it up to it didn't work out."