I know that India is not best pleased; they never have been. We should also remember that during the 1971 war many of the Awami League took refuge in India and then India came to Bangladesh's aid, so the ties there are fairly strong. As you know, India has a very porous border with Bangladesh. People have fields through which the border runs. There is a lot of smuggling there. India has always looked very warily at Bangladesh.
What surprises me even more is the influence of Pakistan, which is practically one continent away. With the advent of the military dictators, who were trained in military colleges in Pakistan, the influence came back. In the first few years there was a great chill between these countries, and rightly so. If you read Gary Bass's book, The Blood Telegram, you will see the enmity that existed and in some areas still exists, which is why the bloggers were able to bring all those people out onto the streets calling for the death penalty for any of the war criminals from 1971.
About China, it is hard to say; I have not much idea. But since I have been a student of the politics of Pakistan and Afghanistan, I can see where the links would come, especially with Pakistan.