His name might not have been well known to the public, but within the series he had earned a lot of respect thanks to his spell with the FIA under Jean Todt.
The 52-year-old Austrian has a busy CV, having worked in a variety of sports before finding his way into motor racing. As such he brings an intriguing range of experience to the job of overseeing the political and commercial aspects of the Faenza outfit.
Born in 1971, Bayer was an F1 fan in his youth, and he grew up watching races on the national ORF channel with his father.
"Niki Lauda was such a national hero, he was bigger than anything in Austria," he recalls. "I know we have Mozart and other famous people, but Niki was somebody that for me was just an incredible person."
After completing a business administration degree Bayer hoped to get a job in motor racing, but he had no contacts and no way in, with a cold call to Bernie Ecclestone's office asking for advice leading nowhere. Instead, his life took another direction.
"I spent a lot of time back then skiing and snowboarding and climbing," he recalls. "And I met some people who said, 'Come and work with us,' which is why I joined the International Snowboard Federation.
"And that was a great experience. I understood quickly that there is a niche where a lot of commercial partners want to get into things like this because they can reach out to a younger audience.
"Snowboarding was very much a mix of sports, culture, lifestyle, music, fashion. We organised snowboarding events, and we then added music festivals. The next step was I created my own electronic music festival in 2005, called Soundcity, which was one of the two biggest in Austria."
His involvement in winter sports led to an opportunity to work with the International Olympic Committee on a new project.
"The IOC created the Youth Olympic Games to remain relevant to a younger audience. It started in 2010 in Singapore, and then in 2012 in Innsbruck at the first winter games I was acting as CEO."
A meeting with businessman and London Olympics deputy chairman Sir Keth Mills saw Bayer move in 2013 into sailing, with his involvement including the Ocean Masters series and the America's Cup. Then by chance, an opportunity arose to work in motorsport.
"Jean Todt is very close to Christophe de Kepper, who is the director general of the IOC," says Bayer. "He was looking for a new secretary general for the FIA. And he called Christophe, who said, 'Well, I know a guy.'
"I met Jean, and he grilled me for three months. I had to do a lot of meetings, a lot of presentations, because he wanted to be sure that I understood motorsport. Obviously didn't have any background other than my passion for it.
"I had to do a presentation for him analysing the strengths and weaknesses of all the championships, their structures, the assets they manage. I guess I got it right, and I convinced Jean and the World Council to pick me."
When he took up the role in March 2017, Bayer received some interesting advice from his immediate predecessor, Jean-Louis Valentin, who was moving into real-world politics.
"The first day he told me, 'Peter, your focus is the administration, rallying, the WEC," Bayer recalls. "Don't get yourself into F1, it will just be trouble!'
"It took me three years to get the full confidence of Jean. But after three years he handed over the keys and said, 'Motorsports, you run it, I'll take care of other stuff.' Which obviously opened the door for me.
"I moved very much away from the sort of admin and rubber-stamping job into a more proactive management style.
"I'd say 80% of my time was engaging and working with the championship promoters on the future strategic direction. I would speak a lot to Alejandro Agag about the future of Formula E - I led the negotiations to make Formula E a world championship.
"I negotiated promotion agreements for the World Rally Raid Championship, and an extension of the World Rally Championship, and moved the European Rally Championship and Rallycross under one umbrella with the German promoters. That was my day-to-day business."
On the F1 side, he was closely involved in the development of the new financial regulations and cost cap, as well as helping to define the 2026 power unit package.
"The financial regs were very, very important to us," he says. "The original idea came from [F1 CEO] Chase Carey, and I understood what Chase wanted to achieve with it.
"And from my business background, I also felt that we could actually make it happen. Because ultimately, accounting is a very precise business, just as engineering work is.
"With the engine regulations it might be funny that I was leading the project, but we started with a strategic group of people, which was Ola Kallenius [Mercedes], John Elkann [Ferrari], Oliver Blume [VW/Porsche], Markus Duesmann [VW/Audi], Luca de Meo [Renault], Jean Todt, and Stefano Domenicali.
"Those were the leaders of motorsport who came together and said, 'Okay, what can we do? How do we keep this relevant, and at the same time attractive?'
"And that's where we started to define the strategic direction of the engine. It's then technical details, but my job was to make sure that whatever the engineers came up with stayed in line with the strategic objective."
Bayer became such a respected player that in 2021 he added the job title of F1 executive director to his wider FIA role.
With Todt's final term as FIA president coming to an end, Mohammed Ben Sulayem was elected in December 2021 on a platform that included creating a CEO role at the FIA.
Bin Sulayem had his own team and own ideas, and Bayer's face no longer fitted. He left the organisation in May last year.
"When Mohammed was elected I never understood how they actually wanted to structure the business," he says. "So I focused a lot on the F1 job. But then came the day when I understood a bit better where this is going.
"I just wasn't as committed anymore. I had a huge responsibility under Jean, and that was sort of cut into little pieces. And at the same time, it takes a lot of energy to be in this F1 business, it's 24/7. And I think you need to be absolutely clear about your position, people need to know who you are.
"And I felt that was a bit ambiguous, really, the new people coming in, new managers, new advisors, obviously, everybody had an opinion.
"I'm a very open-minded and calm person, but if I understand things are not working the way I think they should work, I can be quite strong. And that led to some discussions with people around Mohammed, and in the end both agreed that doesn't make sense like this."
Bayer subsequently undertook some consultancy work for the IOC and for Audi's F1 project before the AlphaTauri opportunity arose, with the initial discussions involving Red Bull owner Dietrich Mateschitz prior to his passing last October.
Talks regained momentum earlier this year as Red Bull looked to reboot AlphaTauri under new management, with a split CEO/team principal arrangement replacing Franz Tost. Bayer will be joined by Laurent Mekies in the latter role.
"I really think is a two-man job," says Bayer. "Unless you're in the business for 20 years like Franz or Christian [Horner] or Toto [Wolff], then you might have a structure underneath that sort of supports it.
"But for a medium to small size team the complexity of supporting technical, financial, media commercial, politics, if you want to be efficient, it's too big for one guy."
The split of responsibilities with his former FIA colleague Mekies is clear: "He's doing race team, technical, sporting, which is his primary focus," says Bayer. "Mine is commercial and business and strategy. And then jointly, we'll do the financial regulations."
Bayer's current tasks include putting the pieces in place for a team name change for 2024, preparing for a move to Red Bull Powertrains/Ford power unit under the new rules in 2026, and ensuring that Faenza works more closely than before with Red Bull.
"For me probably the most important message from the shareholders was that AlphaTauri will not be sold," he says. "So we've got stability.
"I guess there's two reasons, one is an emotional attachment to the team, and it makes perfect sense to have that younger brother within the family, who's taking care of young driver development.
"That will stay, so the purpose will remain, for us to find young talent. We might extend that a bit and go a bit more structured into these areas.
"And at the same time, they said find synergies, work closely with Red Bull Racing, exploit the technical regulations, which currently we don't do - the results speak for themselves!
"But also on the commercial side, on HR development, pathways for technical engineers and managers, there's so many more things we can do together. And that's really the strategic focus that I'm working on."
Moving AlphaTauri's UK R&D base from Bicester to Milton Keynes is one option under discussion that will get the attention of rivals, but Bayer insists that such a move won't become an issue.
"It's about the Chinese walls you build in between," he says. "Look at Haas and Ferrari, for example. And I guess Laurent and I bring that experience to the table – 'Guys, we definitely don't want to do something illegal, but we also know that certain things can be done, because we see it happening left and right.'"
