Bavuma and his charges sealed their first ICC title in 27 years after completing a five-wicket victory against Australia at Lord's on Saturday.
The skipper recognised the efforts his team and coaching staff have put in over the last two years, but knows there is always room for improvement.
Bavuma told reporters: "We hope this is the start of something, there could be more trophies. We have created history but we would like to emulate, if not do better than what Graeme (Smith) and his team did.
"They set the standard and I don't think anyone has reached that yet. I'd like us to be in a position where we can go to Pakistan and India, have victories there and do a lot more.
"We have had a lot of success in this cycle, which we don't look past. But from a longevity point of view, to really get the respect out there as a Test team, we'd like to see where we are in the next two years."
The Proteas started day four on 213-2, chasing a target of 282, but but Bavuma and Tristan Stubbs fell relatively quickly to give the Aussies some hope.
Aiden Markram however played a majestic innings of 136 before being dismissed with just five runs required for victory to leave David Bedingham and Kyle Verreynne to take the Proteas over the line.
As the moment of victory drew closer and heartbreak of previous ICC tournaments were banished, Bavuma admitted to flashbacks of his place in the team being questioned and the burden of being a black African cricket captain in South Africa.
He added: "It was quite tense, even when we got it to 10 runs (needed) we knew anything can happen. When he (Verreynne) scored the runs, I hid my head in my hands, just trying to embrace and acknowledge what we've just done.
"I thought of the experiences I've had in the last couple of years. It hasn't been easy, it's not easy being captain of South Africa.
"All the sacrifice, disappointment, at that moment it really feels worth it.
"When you are going through it all, giving up is always an option in the back of your mind but something wills you on. For me, it's that moment there.
"(I want) to be recognised as more than just a black African cricketer, and to be seen as someone who has done something the country has wanted.
"I will walk around with my chest out and hope it continues to inspire our country."
Aiden Markram believes South Africa's victory in the ICC World Test Championship Final has finally laid to rest the long-standing "chokers" tag - and hopes the Proteas' triumph can inspire a new generation to prioritise Test cricket.
President Cyril Ramaphosa has congratulated the Proteas on winning the International Cricket Council's Test Championship against Australia.
This Proteas team have forever written their names in the folklore of South African cricket after beating Australia by five wickets at Lord's to capture the ICC World Test Championship mace.
Aiden Markram proved to be the Proteas' man for the "big occasion" after a scintillating unbeaten century put his team within touching distance of the World Test Championship trophy at Lord's.
