This news-item is from October 2013, but the Bangladesh issue mentioned is on-going, there has been no meeting of the minds between the Indian and US sides. The disagreement stems over the what to make of the radical Islamists in Bangladesh - the Jamaat-e-Islami. India wants them marginalized, the US wants to them to be let into the mainstream.
This news-item is the only one that I've found that provides an explanation of what the US State Department might be thinking. Supposedly the radical Islamists in Bangladesh are more free-market-oriented; and supposedly they will moderate themselves once in power (though they radicalized further the last time they were in power).
The US appears much more comfortable with the BNP-Jamaat combine, who have made no secret of their radicalized politics. India believes if this succeeds, Bangladesh would be very different as a nation. The politics of BNP and Jamaat have become more radicalized in the past couple of years.
Indian intelligence has detected influences of both Pakistan-based Lashkar-e-Taiba (LeT) and al-Qaida. There is a lot of funding available to these groups from West Asian countries, and some from Pakistan.
The US is less comfortable with Sheikh Hasina's government, especially after the PM's confrontation with Mohammed Yunus of Grameen Bank — the fracas over funding for the Padma bridge project — and also the war crimes tribunal. There appears to be a part of official thinking in the US that believes, according to sources here, BNP-Jamaat have better free market credentials, and that they would move away from radical Islam once they are in power. "They are too far away to have a realistic view of the street," they said.
India is haunted by the 2001 Pyrdiwah massacre, when 15 BSF personnel were massacred by BDR troops in an ugly confrontation. BNP had explained Jamaat's place in government thus: it would be better to have them in than out. But once in government, Jamaat occupied the ministries crucial to furthering their radical agenda. Those years saw the flowering of Jama'atul Mujahideen Bangladesh (JMB) and other terror groups like HuJI. India is opposed to a return to those days.