Bavuma batted through 99 percent of South Africa's innings, in which they were tasked with getting 336 runs to beat the Windies in East London but fell 48 runs short in the end.
The 32-year-old showed guts and grit to reach his career-best score despite the constant fall of wickets around him, and Hope – who also scored 129 on his captaincy debut – gave plaudits to his counterpart.
"And Temba, an innings like that deserves to be a victorious inning but it just so happens that we came on top in the end. I must give him credit. He really deserved to win the game, playing innings like that but there can only be one winner," he said.
Hope also gave credit to Proteas debutant Gerald Coetzee, who took match-best bowling figures of 3/57 in his maiden innings, and tips the 22-year-old for a bright career.
"I saw him bowling in test matches and I was keenly waiting to see how he was going to bowl in this particular ODIs here. But I don't think his surface was quick enough for someone to see how quickly he will bowl. He has a decent runout. Hopefully, he can continue to learn. He has a decent career ahead of him," he added.
The Windies now lead the series 1-0 after the first match was abandoned due to rain, and go into the third and final ODI in Potchefstroom with the comfort of knowing they cannot lose the series.
"It's been a great start, hopefully, the guys can pull through in the end. It's important for us to get a good start. Obviously, we lost the first ODI so now we have a great chance of finishing this series," he concluded.