Nissan has tasked an external committee with helping to improve corporate governance after the arrest and ouster of Ghosn, who faces charges of financial misconduct including understating his compensation by about ¥9 billion over almost a decade.
Mr Bajaj was senior vice president for HR for Nissan's alliance with Renault and Mitsubishi Motors.
Under the terms of his bail - which include giving up his three passports and having no smartphone access to the internet - he needed the court's approval to attend.
"There is nothing to do with the shareholdings and the cross-shareholdings that are still there and still in place", Renault Chairman Jean-Dominique Senard said at a news conference.
Although he was nearly immediately fired as the head of the company when the allegations surfaced, he is still a board member until April 8, when an extraordinary meeting of shareholders is likely to remove him.
Nissan CEO Hiroto Saikawa said in the past he believed that Ghosn wielded too much power, creating a lack of oversight and corporate governance.
Nissan also said Arun Bajaj, who served as alliance human resources chief, will exit the company.
If found guilty, Ghosn, widely recognized as the brains and brawn behind Nissan's rapid turnaround from near bankruptcy since 1999, could be facing up to 15 years in jail. In Japan, preparations can take months.
The new board, which consists of the CEOs of the three company's and Renault's chairman, will meet every month in Paris or Tokyo and oversee various projects, helping to make the companies' operations more efficient, they said.
Conditions for his bail restrict his activities to prevent him from any tampering with evidence.
"Mr Ghosn wants to have some time to mull over what he's going to say", Junichiro Hironaka told reporters outside his Tokyo office after meeting with Ghosn throughout the day.
The other charge relates to an alleged attempt to pass off personal investment losses onto Nissan's books and then paying from company funds a Saudi contact who had previously stumped up collateral for him. It is unclear who will take that job, which has been vacant since November, when Ghosn was first arrested.
Ghosn owns more than 3 million Nissan shares, or somewhat less than 0.1 percent of total shares, according to the most recent disclosure.