Can a black woman marry a man from Bangladesh?
As a disclaimer, I am not Bangladeshi or of Bengali origin, though for the past few years I have studied the culture of South Asia in general and Bangladesh in particular. Further, I was married several years to an Indian, and from that experience alone I can tell you that these cultures are difficult for Westerners to break into and really assimilate.
Another Quoran stated that marriage in the end is a matter of heart rather than color, and he is also right.
Pardon my assumption, but I'm going on the idea that you are North American or Australian-born, or from a Western European country.
These things being said, the culture of Bangladesh is far older than Bangladesh as a nation. There are customs, religious practices and social nuances older and very different from those of the West, and you will be called upon to accept and adapt to things which are not normal in our society.
Consider the joint family. This is still the norm in the subcontinent, where it's not unusual and still quite expected that sons will remain at home with parents and grandparents, even if they are successful and highly-placed wage earners. There is a high premium placed on duty and respect to elders, and a bride is expected to eventually care for her elder inlaws. Marriage is less a union of a man and woman than a union of entire families, and often seen as a duty to God and the society at large.
By contrast, in the West a man who stays with his parents is seen as a loser who can't cut the proverbial apron strings, an underachieving gamer, or a lazy man who still wants Mom to wash his shorts. He would be encouraged by his peers, his woman, and sometimes his own parents, to move out.
In the West, living independently is a sign of success and maturity. In the South Asian societies, it's a sign of selfishness and disrespect to the generations who cared for you when you were helpless and educated you when you were immature or ignorant.
The joint family structure may be the most glaring example of our cultural differences, being one of the major things touched upon in basic social studies classes. But it's honestly the tip of the iceberg. There are protocols of courtesy and language based upon age and rank, religious protocols, standards of dress and a small army of other things that you'll not only need to know, but need to apply if the family would even consider consenting to a marriage.
And that's another thing...you'll need to know the language, at least get a decent working knowledge. The extended family is not a bunch of roommates splitting rent. It's a functioning unit, and without communication a person does not survive in it. Even among the immigrant communities, a lot of the senior population don't speak English. Language is as much tied into the Bengali culture and experience worldwide as religion and social customs. Much of your acceptance into this community is going to depend on your appreciation for, and willingness to learn, pure Bangla or your spouse's regional dialect.
It's difficult. But not impossible.
Best of blessings to you on this journey.