Bangladesh, like a lot of other third world countries require an awful lot of work to become, 'first-world' ready, thoughts we take for granted are condemned in such societies, but if they were to continue as-is, could they become a superpower? Would their current way of thinking hinder them to do so?
Being a superpower is not just a measure of hard power. Nations as diverse as ancient Sparta, Sweden in the 1700's or the former USSR had lots of "hard" power, but ultimately the ability to raise and project military power amounted to a flash in the pan, and no lasting legacies.
The United States, and the British Empire before it were superpowers because they had a very solid foundation of culture, institutions and society which was not only secure and stable at home (allowing for long term planning and economic growth), but was also attractive to other nations and people's.
Stable and secure cultures and institutions take a lot of work to create, and even more to maintain (which is arguably why the British Empire no longer "rules the waves" and the United States is floundering vis a vi its global competitors). The other thing that needs to be addressed is to find a workable "Grand Strategy" that encompasses, protects and expands the nations interests.
It may be possible for small nations like Bangladesh to rise to superpower status, we know that the Serenìsima Repùblica Vèneta was a city state capable of competing with the Ottoman Empire, the UK is a relatively small nation compared to many of its former European rivals, and Sweden and the Netherlands were also once great "Powers" in Europe (the Netherlands even having a global Empire). For this to happen, Bangladesh or any other would be superpower has to do a lot of work to build strong and stable institutions to create a strong and attractive Bangladesh first (a clean government and judiciary are good first steps; stamping out corruption would make Bangladesh 100% stronger just by itself).
As for a Grand Strategy, consider the United States Grand Strategy is to:
1 Ensure no rival Powers exist in North America
2 Control the sea approaches to the continent
From these considerations, America can create and grow a secure internal peacetime economy, and use its control of the oceans to protect and enhance oceanic trade for the benefit of American traders. This also allows America to project forces around the world as a result of American Grand Strategy.
Bangledesh would have a much more difficult balancing act. It is surrounded on all sides by potential rivals, most of them much larger, so a great deal of time and energy must be spent on either using diplomacy or force to protect themselves from potential rivals. Naval and trade considerations are also constrained by the position of the nation relative to others and geographically by its position in the Indian Ocean. Like many land empires, Bangladesh would have much of its potential siphoned off dealing with the neighbours, which would take a lot of steam out of its potential to become a superpower.
So while circumstances would seem to be against it right now, there is no reason for Bangladesh to languish forever as a third world nation. With the right internal drive to reorganize its institutions and culture, and the right circumstances to keep external pressures off (for a while), there is a possibility of Bangladesh becoming a true middle power, much like Canada was, and perhaps even a great power like the Serenìsima Repùblica Vèneta was in its time.
It's probably never going to happen.
To be a superpower means the country needs to hold a significant part of the world's economy (in % of the GDP) and of the world's military power. Right now, according to the definition above, the United States of America do not meet these criteria anymore as other country like China, Saudi Arabia, India and other developing countries are taking a large share of the pie. It became a superpower more or less after WW2 but lost it a couple of years ago.
That being said, while it's impossible to have Bangladesh become a superpower in the following century, they could become one eventually. Even a rather small country can rule the waves or the stars. It could happen if they get to lead in the technology research, giving them an advantage over the other. Although, I doupt they could manage to get advanced enough to eclipse the other countries. We live in an age of information and exchanges: it's not possible to hide new discoveries for long.
For the time being, there is a much more likely candidate for the job: China.
Bangledesh can become a super-power if two conditions are met.
The Roswell event and all other UFO-crash stories are fictional, so no other nation on the planet has access to alien technology.
A real Roswell event occurs in Bangledesh and technologies of significant military, industrial and economic value are successfully salvaged.
In what sense do you mean the question? Is the question, Is it physically possible, i.e. is there something about the nature of the land making up Bangladesh, or about it's location on the globe, that makes it impossible for them to become a superpower? Or is it, Is it psychologically or culturally impossible, i.e. do the Bengali people just not have the right mind-set to become a superpower?
If it's (a), I'd guess the answer is that there is nothing stopping them. Portugal became a superpower in the 1400s, Spain in the 1500s, Britain in the 1700s, etc. None of these countries had any obvious abundance of some crucial natural resource or any such. I don't see why geography or resources would prevent Bangladesh from becoming a superpower.
If it's (b), then in one sense I'd say that the same things that keep them relatively poor now would likely continue to keep them relatively poor.
What makes countries rich and powerful? Well, historians debate that and have written books on the subject. In the short run, an aggressive and capable ruler can lead his nation to conquer his neighbors and build an empire, even if his home nation is relatively poor. Alexander the Great and Genghis Khan come to mind.
To build a rich country requires a nation with many people with an entrepreneurial spirit, a philosophy or religion that embraces science and technology, and a government that allows people to pursue these things. That's pretty much how the Greeks, Dutch, British, and Americans did it. Could Bangladesh adopt such ideas? There's nothing physically stopping them. I think it's up to them.
This would happen quite naturally following the simultaneous economic and military collapse of every other nation on Earth with the possible exception of, maybe, Somalia and Burundi. Otherwise, it will take some cleverness.
The climate and weather patterns of Earth will probably change catastrophically in the next few centuries. If I were a leader in Bangladesh I would found a multi-decade program to predict and exploit these changes. Places that are inhospitably dry today may become watered and fertile, or cold lands that nobody wants now can be profitably colonized before they warm up.
For example, the people of Bangladesh have been exploiting the seacoast and have made some advances in fish farming. Perhaps they could learn to make economic use of the sea floor, especially in shallow inland seas, which Bangladesh is likely to become in the next century or so if global warming continues.
Of course to become a superpower, as opposed to just a nice place to live, Bangladesh will need to develop a rapacious attitude toward other countries, coupled with the wisdom to refrain from antagonizing their nearest neighbor India, who will remain too powerful to mess with for the foreseeable future.
So, in short: invest heavily in the planet as it will become, not as it is or how we would like it to be; exploit the hell out of the seacoast wherever in Bangladesh it ends up; and colonize and enslave Somalia and Burundi.