Ireland are ranked 10th in the ICC ratings - thanks largely to their exploits at last year's World Cup when they caused a sensation by reaching Super Eight stage.
The Irish famously won their Super Eights match in Bridgetown, by 74 runs and Bangladesh have not won in 14 ODIs since the World Cup.
Simmons' side warmed up for this week's three one-day games against Bangladesh by comfortably beating the United Arab Emirates in a four-day Intercontinental Cup clash in Abu Dhabi last week.
Bangladesh morale is low after their dismal run over the last 12 months and the visitors will be optimistic about their chances in Tuesday's game.
In their most recent contest of Friday, Bangladesh were hammered by seven wickets by South Africa with the Proteas registering the necessary 144 runs with 16 overs to spare.
Ireland will face Bangladesh again on Thursday and Saturday.
