When thinking about what to wear in Bangladesh, the first consideration that should pop into your mind would obviously be that of climate: this is a subtropical country, warm and humid for most of the year and endowed with only the briefest of winters and a still-hot rainy season. This should indicate the first fabric of choice for your sartorial selections in this country: that is, cotton.
Cotton is generally preferred by the locals themselves, who share a few fashion circumstances with the abutting regions of India. Saris and shalwar kameez are popular garments in Bangladesh, and a great many tourists passing through the area actually do opt to wear them. This hardly means you are going to be required to wear them, of course, for Bangladesh is fairly tolerant of other cultures, all things considered. In fact, despite its predominantly Muslim demographic, it is perhaps one of the most (relatively) liberal places in the region.
Hence, you shall be certain to see even the locals wearing quite a number of Western-style clothes, including fairly slim denim jeans and trousers for the women. This indicates that visitors may wear such things as well, although a caveat should be kept in mind: females should still take extra care with their dress to ensure that they do not attract unwanted attention. Granted, given the temperament of Bangladeshis and their intense curiosity about foreigners (travellers are so rare in the country that one passing through the rural areas generally has the appeal of a marvellous travelling circus for the locals), you are going to be attracting attention whatever you wear, but the goal is to prevent that attention from turning negative. Most Bangladeshis are very friendly, even if they are prone to staring with near-childlike curiosity at foreigners, and it is best not to turn those childlike stares into ones of disapproval. If you are a female passing through the country, take care to wear clothes that do not show too much flesh.
So which parts of the body are permitted to be on display, as it were? Obviously, the feet, the lower parts of the leg (near the ankle), the arms and hands, and the neck. As far as skirts go, do not wear things that go above your knees-staying a good few inches below the knees is actually best. As for tops, take care not to go with plunging necklines and avoid baring your shoulders as much as possible: a plain T-shirt would suit most purposes. And as for footwear, anything goes, culturally speaking, although it would be best to wear something more sensible than fashionable: not all roads are paved and some of those that are paved are also craggy. Add to that the heavy rains and flooding that constantly threaten the country and high heels and delicate shoes spell disaster.
When thinking of what to wear in Bangladesh, be certain to check out the season of your trip. March to June sees the country hot and humid for its summer, so wear cotton and lightweight cloths then, and November to February yield its brief and mild winter, which shall often require only a very light jumper or coat. The June to October months are those of its rainy season, which people should generally avoid and which also feels hot despite the constant showers.