Bangladesh means very little from a strategic point of view. As it should be. But there are things going on.
In India's view, Bangladesh presents more of a nuisance. By looking geography, Bangladesh basically cuts in right between the north east states from the mainland. They only have the "chicken neck" to connect them.
That part of the country had been wracked by various insurgencies since the 60's, and still have security vulnerabilities from them. ULFA, Bodos, Nagas (the very first insurgency if I'm not mistaken).......you name it. Yes, there have been improvements, but still they have security vulnerabilities.
Given the security situation and the geography, common sense would indicate that India needs the cooperation of Bangladesh to counter the various insurgencies coming from the north east.
Not to mention, the sheer size of the border measuring 2,429 miles. And "scattered" everywhere. That makes it a porous one. One where those insurgents can take cover easily within the vast, untamed jungles. India also shares the largest border with Bangladesh as well, not Pakistan or China.
India is not worried about BNP? I'd be surprised if they aren't. The AL will assure India's security. In fact, there may be a strong correlation between the AL staying in power, and at least some degree of security improvement in the north east. But it's not like there aren't any insurgents hiding in Bangladesh. There were reports of their presence. An unrealistic expectation. The problem lies with the north eastern communities themselves, and not with Bangladesh, China or Pakistan. Or even mainland India for that matter.
What about Jamaat? They despise them, and perhaps would like them eliminated to make their influence more......meaningful. They fought hard in 71', and seeing a party that opposed separation of Pakistan as an insult to their honor. Jamaat itself saw India as bullying, and perhaps that's what they are all about. It's too small of a party to make any major impact. Nonetheless, it is a comparatively well organized party.
What about America? The visiting American officials have said many times that they do not want to see violence. What does that mean?
Given that the AL comes to power after the next elections, they'll cut Jamaat like grass with a lawn mower. What will Jamaat do? Their members will go underground where they can mingle with more powerful groups. Armed too. The Hefajotis have massive support from Bangladesh's poor rural community as well.
Simply put it, even 1% of Bangladesh's population is a lot. We know that America is at war with an enemy that cannot be seen, or heard from. But it can indeed kill. Would they want to see more numbers added to their already weakening strength? Very unlikely. They want Jamaat to remain as a legal party as it always had been. It does not matter if they are bad or a minority.
People who say that Jamaat should be permanently banned do not understand that one of the very basic fundamentals of a democracy is to let the minority survive. And what the AL is doing, is not democracy. A tragic reminiscence of the early 70's.
If Modi is to come to power, the AL and the Sheikhs would be left more vulnerable since they do not have any form of understanding with the BJP. In fact, BJP works very little in regards to Bangladesh. The only thing in their mind is deporting illegal immigrants. But, that doesn't not mean that would be the end of Indian bullying either. It might increase in the region.
Interestingly, assuring Modi's security from the Indian Mujaheddin is said to be one of Indian security establishment's greatest challenges. Even as an opposition leader, they have to work quite a lot for his security. Him coming to power may even pose greater security challenges from the entire region.