Not, it seems, if James can help it.
The custom bike builder just bought a $1.9 million-dollar estate in Austin, Texas, the same town where Bullock, 45, owns a home and the couple once lived together.
"He's like that boyfriend you can never get rid of," Popeater gossip columnist Rob Shuter told ABCNews.com. "Part of me admires his determinism. But when does it become a stalker? This is just a little bit creepy now. Following her around isn't going to win her back."
James, 41, has made no secret of his desire to win his ex-wife back after she split from him in April amid reports that he had multiple affairs.
Just over a month ago he told Vicki Mabrey of ABC News' "Nightline," "I still really love her and care about her."
Complicating James' move to Austin is his custody battle with ex-wife Janine Lindemulder, the mother of his youngest daughter Sunny.
The two sides were in Orange County Superior Family Court Monday, where Lindemulder is asking a judge to rule that James not be allowed to move to Texas with Sunny. The hearing is expected to continue through today.
In court documents filed earlier and obtained by TMZ, Janine claimed that Jesse's reasons for wanting to move to Texas with Sunny -- "so his children could continue their relationship with Sandra Bullock" -- were "wholly unjustified."
Pointing to Bullock's move to Austin, Lindemulder said, "Certainly if that relationship were that important to Sandra, she would have stayed in California."
Since completing a month-long stint in rehab, James has been trying to rebuild his life and win back his wife.
A friend of his told People magazine in May that James does not believe his relationship with Bullock has "reached the final chapter."
"He is not giving up hope that Sandra will come back to her family," the friend said.
Final Chapter for James and Bullock?
If James is hoping to write a new chapter in their relationship, it appears Bullock is ready to move on.
In June, at the MTV Movie Awards, Bullock stole the show when she locked lips with Scarlett Johansson.
"Now that we have done that," Bullock announced afterwards, "can we please go back to normal?"
"Sandra wants things to get back to normal," Shuter said. "She can't put that period at the end of a sentence. Every time she tries to end it, he does something that picks the scab off this wound."
In May, James, planning to move to Austin, put up for sale the two-story California beachfront property that was the couple's home during their nearly five-year marriage.
James is no stranger to Austin, having lived there off and on with Bullock. He also owns Austin Speed Shop, a custom-car business.
But Bullock, who also owns several businesses in Austin, has lived there longer and, as the wronged spouse, has the community's sympathy on her side.
"There's a level of affection that I've never seen before," said Shuter, who spoke with many of the locals. "The locals are worried. Given the amount of pain that Jesse has obviously caused her, it's not going to get any easier for her. A lot of people are worried it might get too much for her and that she might pull up roots and move."
Bullock recently purchased a home in New Orleans, the birthplace of her adopted son Louis Bardo.
James, who began the adoption process with Bullock before their breakup, has spoken about wanting to have a relationship with Louis, as well as to have Bullock maintain her relationship with his three children from previous marriages.
But Shuter said the idea that James would need to live in the same town in order for that to happen is just a ruse. "It's not a plausible excuse," he said. "Their wealth makes the rules different. If he wants to hire a private plane for the kids to hang out with Sandra, he can."
Bullock appears to have the left the door open for James to have a relationship with Louis. "I really don't know how our paths will intersect in the future, but the father I have known Jesse to be with all the kids is one that I hope Louis can experience one day, no matter how Jesse and I go on with our lives," she told People in April.
Last month, Lindemulder cast doubts on James' motive for moving. She told In Touch Weekly that James had said that if he couldn't reunite with Bullock, "he's got a 'backup plan' with another girl in Austin."
"Imagine him saying he is moving to Austin to be a dad to 5-month-old Louis and to be there for Sandra, uprooting Sunny -- and it's because he might be pursuing mistresses," she said. "He could be off his rocker."