Rahim said he wanted his team to build on their form in home matches, including Test wins over England and Australia in the past year.
"Bangladesh has been playing really well in the last couple of years," he said.
"The first target is to keep that intensity going. When we are playing at home we are really confident.
"It's not going to be easy, but this is our next step. We want to do well in Africa as well. It is a great opportunity for us."
Rahim admitted that the unavailability of all-rounder Shakib Al Hasan for the two Tests against South Africa was a blow.
"Shakib is a special player and no-one can replace him," he said.
He acknowledged that meeting the challenge of South Africa’s fast bowlers in local conditions would be crucial.
"How we cope with the fast bowlers is key to our success," he said.
"But players like Tamim Iqbal, Mahmudullah, Sabbir Rahman and Mominul Haque have improved a lot as individuals and hopefully they will take their responsibility to the middle."
Rahim said he expected good performances from his bowlers.
"They are inexperienced but skilful and if the wickets offer a little bit of spin, our spinners can do well."
Bangladesh declared at 306 for seven Thursday in the opening day of a three-day warm-up against a South African Invitation XI at Willowmoore Park in eastern Johannesburg suburb Benoni.
The home team were 21 for one at the close.
Opening batsman Tamim was forced to retire hurt with a thigh muscle injury after facing just 13 balls.
Tamim, a veteran of 51 Tests and the team's all-time leading run-scorer, made five runs before leaving the field in the fifth over.
Team manager Minhazul Nanna said the batsman had suffered a strained right thigh muscle.
He left the field as a precaution and his condition would be assessed Friday following a scan.
Bangladesh will play two Tests, three one-day internationals and two Twenty20 internationals during the tour.
bangladesh vs south africa 2017Mushfiqur Rahimshakib al hasanSouth Africa vs Bangladesh 2017Tamim Iqbal
First Published: September 22, 2017, 4:41 PM IST