To be quite honest, my knowledge on India's policies are quite limited, I'll have to review this before I give my point of view.
Let me give you a snapshot:
1- Ever since Bangladesh came into existence, thanks to our military, there has been an India friendly government in Bangladesh in general, called Awami League (popular league). Now this party over the years has been involved in local corruption there and therefore has become a problem for Bangladeshis. But somehow, they still continue to win elections. Now there is a fringe element of radical islamists who regret the separation of Bangladesh from Pakistan (Refer 1971 Indo-Pak war if you are unaware). They are the theocratic fanatics who loath the Hindu and Buddhist Bangladeshis and hate India all the more for the same reason. They feel that those who are no Muslim are all Indian 'agents'.
For years, these guys have been trying to come to power but have failed in their elections because the general crowd doesn't elect them. Frustrated with repeated electoral failure, they think that we have 'installed' the Awami League as a the perennial rulers of their country. It is true that when Bangladesh became independent, the AL had strong support from our country for their freedom, but years later i.e. now, it is mostly their internal politics. To the world, they project that they are a 'small nation struggling against big bully India' to get the sympathies while their radical groups create hell in Indo-Bangla border through migrating illegally and attacking locals. We don't like it so they get pissed. Beat that logic.
2- Regarding Pakistan, you know too well what our relations with them are like.
3- Nepal: Culturally same, we have invested a lot in there and therefore have a considerable influence there in terms of friendly relations. Nepali far-left want to use anti-India agenda as they have relations with communist terrorists in India. While the Nepali nationalists are there, they don't have any significant seats in Nepali Parliament. To make a political issue, they constantly rake up the 'big India bully' which their ruling government doesn't think so.
However, our historic ties are excellent always. We have an open border policy with Nepal and Bhutan, which means Nepalis and Bhutanese people can stay, work and live in India as long as they want and vice versa. Nepal's national security is our collective responsibility.
4- Our ties have significantly improved with Sri Lanka after Mr. Rajapakse's visit to Delhi 2 weeks ago and both nations are willing to forget past bitterness and move forward with strong relations.
5- Afghanistan has strong relations with India and we enjoy warm ties with both Afghan people and the government.
6- Mauritius: Another friendly country. It is an indianized country with robust commercial and economic relations with us. We also are responsible for their security in the Indian Ocean.
7- Bhutan: A very staunch ally, Bhutan's hydropower capability has a robust investment from our private corporates like Tata Power. Their and Nepali rupees are pegged to our currency. Very cordial relations between the two. Bhutan's national security is our responsibility.
8- Maldives: Strong ties historically, except once in the middle when the previous government of Mr. Nasheed was kicked out and the new government became anti-India. However, things have warmed up now and differences are settled. We are responsible for their security.