Saturday's 176-run flogging of Australia in Cape Town not only kept the Proteas' almost seven-year undefeated run at home alive, but also means they replaced Pat Cummins' side at the top of the ICC rankings.
Already the World Test champions after beating Australia in last year's final, Bavuma revealed a desire to silence critics who claimed it was a "fluke".
The fact South Africa are on top of the Test tree for the first time in 12 years is an incredible showing of desire and willingness from the players.
It was only two and a half years ago that the Proteas sent a third-string team to New Zealand, with Cricket South Africa prioritising their domestic T20 league.
South Africa also didn't host any red-ball matches last summer, with this series against Australia their first at home since the Test Championship win.
But it is clear players want Test success with Bavuma as captain, winning 13 of 15 matches under him with one draw.
Brought in as captain after South Africa felt bullied and beaten by Australia in 2022-23, he now has series wins over India away and Australia at home.
"We've surpassed a lot of the things that we put to ourselves, but it's just because of that belief and that oneness that we have as a team," Bavuma said.
"Did I think two years or two and a half years (ago) we'd be in this position? Probably not.
"But like I've always said to the team, we'd like to see after four years what it is that we've achieved."
South Africa have now leapfrogged Australia into the top two in the race for the Test Championship final, with series against Bangladesh, England and Sri Lanka to come.
They also now have the star power to be the best.
Marco Jansen's player-of-the-series efforts now have him as the ICC's top-ranked bowler and allrounder.
Simon Harmer is a legitimate star, spinning the Proteas to wins over both India and Australia with six-wicket hauls.
Kagiso Rabada remains one of the world's best quicks and broke open Australia's top order on Saturday on the way to having them all out for 111.
Bavuma and his story are also crucial to their resilience, after South Africa were well behind in the second and third Tests but found victories in both to win the compelling series 2-1.
"You always want to leave a bit of yourself in the team," Bavuma said.
"Resilience is a word that we speak about as a team. Resilience is something that features massively within my own career as a cricketer.
"It was 15 days of just pressure. As a team, we can only really get better from this type of experience."
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