Clare Shillington and Laura Delany both made 37 as Ireland were bowled out for 144 after 47.1 overs of their innings.
Bangladesh replied with 145-3 off 39.1 overs to win with 65 balls to spare, Sharmin Akhter top-scoring with 52.
Ireland must win their remaining two matches against Pakistan and South Africa to maintain qualification hopes.
Ireland retained their one-day international status by making the Super Six, from which the top four qualify for the World Cup this summer.
After being put in to bat by Bangladesh at the Colombo Cricket Club, the Irish women were dealt an early blow as Cecilia Joyce (3) and Kim Garth (0) both went cheaply.
Meg Kendal returned from her hamstring injury to make 16, sharing in a third wicket stand of 45 with Shillington, who struck four boundaries and cleared the ropes twice in an entertaining 37 from 36 balls.
Both fell in quick succession and it was left to skipper Delany and Isobel Joyce (24) to rebuild the innings with a stand of 44.
Having reached 106-4 with 19 overs remaining, Ireland looked set for a total approaching 200, however the innings faltered in the final third, as they slumped to 144 all out.
Jahanara Alam (3-21), Panna Ghosh (2-16) and Khadija Tul Kubra (2-26) were best with the ball for Bangladesh.
Ireland needed quick wickets in the Bangladesh chase, but their attack was blunted by a steady opening stand of 40 between Sharmin Sultana (22) and Sharmin Akhter.
Gaby Lewis (1-31) dismissed Sultana, and when Isobel Joyce ran out Islam for 2, Ireland were back in the contest at 52-2.
However Akhter hit a fine half century from 86 balls, adding 53 with Morgana Hoque, to ensure Bangladesh quickly regained control.
Although Akhter was dismissed by Ciara Metcalfe (1-33), by that stage just 39 were needed, and Hoque (34 not out) in conjunction with Rumana Ahmed (24 not out) steered their side safely home.
Ireland are next in action when they face Pakistan on Friday, before taking on South Africa on Sunday.

The annual hand ba' game took place in Jedburgh on Thursday - one of a number of Scottish Borders towns to stage such events on their streets.

Setting off at a leisurely pace through the west end, the former governor of California promptly began cycling on the wrong side of the street.
The Terminator star was in the capital to attend a black-tie dinner in his honour at the Edinburgh International Conference Centre.
The Hollywood star is often spotted cycling at home in California.
He shocked London commuters last year when he jumped on a Boris bike to enjoy a sightseeing tour.

On Tuesday the captain of a UK-registered vessel was fined £10,000 for unlawfully fishing in Manx waters.
It follows the prosecution at Douglas courthouse last week of a Scottish fisherman who was fined £15,000 for breaching Manx regulations.
Richard Ronan MHK said the "significant fines send out a clear message".
The Deputy High Bailiff ordered both skippers to forfeit their catch of King Scallops worth nearly £5,500 each (about 90 bags).
Both vessels were routinely boarded by officers from the Manx government's fisheries protection vessel Barrule before being escorted back to the island and detained.
Mr Ronan, the Minister for Environment, Food and Agriculture, said: "The Isle of Man is committed to the protection and development of stocks of shellfish within its territorial sea and is vigilant over illegal fishing activity.
"These significant fines must act as a strong deterrent."
He added that the Isle of Man "welcomes responsible skippers" with registered vessels to sustainably fish in the Isle of Man's territorial sea with the appropriate licence.
Manx territorial waters extend out to 12 miles around the island's coastline and contain a number of restricted zones.
Ireland's hopes of qualifying for the World Cup appear remote after suffering a seven-wicket defeat by Bangladesh in their opening Super Six match.
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All images by Dougie Johnston.
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Action hero Arnold Schwarzenegger has taken to the streets of Edinburgh for a morning bike ride.
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The prosecution of a second UK skipper in a week for breaching Manx fishing regulations sends a "clear message to the industry," a politician has said.