Bavuma hit 113 in a total of 354 for five after South Africa were sent in to bat. Ireland were bowled out for 148 in reply.
Ireland captain Will Porterfield's gamble did not pay off as Bavuma and Quinton de Kock (82) punished the Irish bowling in an opening partnership of 159.
Porterfield described his team's performance as "disappointing" and bemoaned early chances which went astray.
JP Duminy and Farhaan Behardien both hit rapid half-centuries to take South Africa to a total that always looked likely to be well beyond Ireland's reach.
Off-spinner Duminy completed a good all-round day by taking a career-best four for 16.
Ireland were without experienced batsman Niall O'Brien, who slipped in his hotel bathroom on Sunday morning and suffered a head injury.
They will play Australia at the same venue on Tuesday before South Africa meet Australia in five one-day internationals, starting at Centurion on Friday.
The South African team included three new caps. Bavuma, established as a middle order batsman in the Test side, was given his chance as an opener in the absence of Hashim Amla.
"It was a good outing," said South African captain Faf du Plessis, "and all three debutants got into the game."
Bavuma, who was dropped on one when he edged Peter Chase to Kevin O'Brien at second slip, took advantage of the let-off with a composed innings, reaching his fifty off 54 balls and his century off 110 deliveries. He was out 13 balls later after hitting 13 fours and a six.
On a slow pitch, South Africa struggled to increase their scoring rate in the middle overs but Duminy (52 not out) and Behardien (50) gave the innings impetus with a fifth wicket stand of 87 off 40 balls before Behardien was caught on the boundary off the last ball of the innings.
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