"If you give them a chance they will pounce on it," Smith told a news conference on Friday. "You've got to start well against them and put them on the back foot as early as you can.
"If you give them a sniff they've got players who have, under (coach) Dav Whatmore, learnt how to win games.
"They're young, and they don't think about the situations that they're in. They play with that sort of freedom."
Bangladesh were at their most confident in their five-wicket win over India in a Group B match in Port-of-Spain, Trinidad on March 17. That shock reverse led to the 1983 champions' first-round elimination.
Since then they have lost momentum and they were beaten by 10 wickets and nine wickets by Australia and New Zealand respectively in their last two matches.
Bangladesh captain Habibul Bashar hoped his men would bounce back against the South Africans, who like Australia and New Zealand, are also among the favourites to win the tournament.
"I don't think we played our best cricket in our last two games and I believe we can improve," Bashar told a news conference.
"Our game plan is to keep as many wickets in hand as we can, and if we bowl first we would like to restrict them to a total we could chase."
AMID SPECULATION
Bangladesh have had to prepare for the match amid speculation that Whatmore could be in line to replace Greg Chappell as India's coach.
However, Bashar was quick to deny that Whatmore's situation was having a negative impact on the team.
"The way Dav is working with us, he really didn't show that he wants to leave us," Bashar said. "He's never given us any indication that he's not enjoying his time with us.
"We are in the middle of a very important tour and everyone is focussed on that, including Dav and the players."
Smith briefly entertained the prospect of what he said would be a "dream" final between Australia and South Africa.
"I guess you would want a South Africa-Australia final," Smith said. "Certainly from our point of view that's what most of our young guys dream about growing up.
"But we are not mapping out where we want to be, we want to get ourselves into the semi-finals first."
The seven-week World Cup culminates in the April 28 final in Barbados.
