The world number one-ranked team have won both second-stage Super Eights matches against Sri Lanka and Ireland and will be well placed to make the last four with another win at the Providence Stadium.
Bangladesh, who progressed from the group stage after a surprise win over 1983 champions India, have lost their two Super Eights matches to defending champions Australia and New Zealand by ten and nine wickets respectively.
Smith said his team were not taking the Bangladeshis for granted even though they were not expected to reach this stage. He was wary of their youthful innocence to play with freedom and confidence.
However, Smith could not resist a brief look into the future should his team progress to the semi-finals as expected. He was already looking at a "dream" final with defending champions Australia.
"I guess you would want a South Africa-Australia final," Smith told reporters. "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."
Bangladesh, meantime, have had their preparations hit by injury that forced bowler Tapash Baisya home and also speculation linking coach Dav Whatmore with the vacant India job after Greg Chappell quit on Wednesday.
Captain Habibul Bashar, though, played down the rumours and also told how Whatmore's commitment to the team should not be in doubt.
"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."
Neither team reported any late injury problems. The seven-week World Cup, the first in the Caribbean, culminates in the April 28 final in Barbados.
