What happened to Roy Hobbs after the shooting?

It has been years since I read The Natural (Bernard Malamud, 1952), and I do not remember the answer to your question, but Wikipedia suggests that the book never answers it anyway.

We are told that 15 years pass between the shooting and when Knights Co-owner Judge Banner finds Roy somewhere and hires him, but what Roy was doing in those years does not seem to be addressed.

Roy's character is more flawed in the book than in the movie, and the ending of the story is very different. Even if the answer to your question were in the book, it would not be right to assume the same events took place in the film's universe.

https://en.wikipedia.org/wiki/The_Natural

What I get is more inferred than canon, so feel free to down-vote for that.

Obviously, an attempted murder/suicide after a liaison with an anonymous serial-killer-groupie would be considered especially scandalous for the time period. When Max Murphy reveals that he found out about the story, and has police file photos, he's pretty much implying that Roy's career would be ended by the revelation.

Connecting the dots, when that happened, Roy knew or was told that no major league team would touch him, and that his dreams were dead. So he left baseball.

Also, given that the bullet was still in him, and that it gave him problems, so many years later, it is highly likely that he was told that he could not play the game any more.

He specifically states that he "sort of" gave up the game, and that he bumped around before returning to the Oilers (he was only there two weeks before getting signed). The script doesn't imply that he was playing, undercover, in the minors, like Shoeless Joe in Eight Men Out. He was out of the game for sixteen years, got back in with the Heeber Oilers, a semi-pro team, and said he played in high school before that. He doesn't mention any other semi-pro or minor league teams.

Script/Transcript of The Natural

ok, I think, just maybe, he went to prison for the death of the Bird lady, because back in those days you didn't go to a lady's room.... so I think maybe he recovered from his gut shot and did some time.

The big gambler claims he "lost $100,000 on 3 pitches". The gambler referred to the time the Whammer was struck out by Hobbs in an open field. The gambler stated that he messed the guy up, who cost him the bet, a week later and ruined him. The gambler hired the hit-woman. In typical fashion the hit woman his killed so there isn't a witness. Hobbs states, in the film, that you can't play while in jail. He did some time.

In the film, Roy tells Iris during the walk that after he was shot, he spent two years in the hospital. When he finally got out, he was told he couldn't play baseball, lost all his confidence, and did various jobs mostly in the Baltimore area. He was basically a regular person with PTSD and no goals just living day to day in menial jobs for 10-12 years. Understandably has no trust in women. He finally decided to try baseball again after 16 years.

I used to wonder why he never tried to contact Iris in all that time but then thought more about it -- to him it was just his childhood best friend that had (in his mind) moved on after he left. I doubt he wanted her to know about the incident, so after two years in the hospital, she had probably gotten married and started her new life. Again, he lost all confidence and fell into a rut in Baltimore. And most importantly, he had no idea she was raising his child. In fact, if it weren't for that child, Iris might have reacted the same way in the coffee shop when she heard his name, but doubtfully would have approached him the same way. She would have probably been married with someone else's kids, and perhaps after the meeting in the coffee shop and her goodbye in the taxi, that would have been the end and she wouldn't care if he never told her what happened.

In the book, he just plays semipro all that time until he finally gets his chance years later. Iris doesn't even exist until he is on the Knights and is not his true love in any way. Just some nice woman that he had sex with as a pro after memo dumped him, who he discarded once he found out she was a grandmother. Roy was a bit of a jerk in the book and it caught up to him in the end, when he finally tried to win, but it was too late.