Last month, United States officials told Bangladeshi authorities that they had information suggesting that terrorists linked to the Islamic State were preparing to ramp up activity within Bangladesh’s borders. In the days that followed, a series of unusual attacks and threats seemed to substantiate the warnings. An Italian aid worker was fatally shot in this city’s diplomatic zone. A Japanese agriculturalist was shot in the north of the country. Last Saturday, a bomber sneaked into a huge gathering of Shiite Muslims, weaving through rings of police officers before killing a teenage boy and wounding dozens of other people.