Most internal transport within Bangladesh is incredibly cheap, particularly for locals, so everyone uses it all the time, and hence most journeys are crowded. On airlines, foreigners pay higher fares but they are still cheap by most standards. The thing which distinguishes Bangladesh from most countries is the presence of a well-developed and much-used system of river boats. These can be quite an experience.
I will try to briefly summarize ways of seeing the country.
Bus: I must be completely up front and say I am not a great fan of bus travel in Bangladesh. The problem is the amazing number of accidents that occur which would indicate that Bangladeshi bus drivers are some of the most reckless in Asia. If you spend more than a few minutes on a major highway, you will see that for yourself. Almost-out-of-control battered buses will roar past every few minutes, often scattering people and livestock in the process. I don’t think I traveled anywhere in the country without seeing the aftermath of an accident. If you must travel by bus, the air-conditioned coach liners are the most comfortable and safest. Ordinary buses are often incredibly crowded with bags, people, and chickens filling the aisles and sitting on the roof. Although it might appear to be a novelty, don’t follow the locals and use the roof. Numerous people get killed each year by tree branches or by falling off.
Train: There is quite an extensive system of railways within the country, but rail travel is hampered because there are three different gauges and because there are still places where you have to cross rivers by ferry rather than by bridge. Trains, however, are much less stressful than buses, and there is far more room at least in first class. Intercity trains are frequent on some routes and are relatively clean. First class is good, while second class with reserved seating is cheaper and acceptable. There are generally no buffet cars, but snacks are available from railway staff and at stations. On local trains, ordinary second class (you cannot book a seat) is often crowded and uncomfortable.
River boat: Ferry boats are popular and are operated by the government (Bangladesh Inland Waterway Transport Corporation) and various private operators. River travel can be relaxing and is comfortable in first class but is less so elsewhere. On many boats there are four classes, with deck class being the cheapest--it gives you nothing more than the right to occupy a space on the deck. One trip is particularly noteworthy. That is the “Rocket” service between Dhaka and Khulna. The trip takes about 26 hours and can be fun. First-class passengers get cabins with bunk beds and a washbasin. Bathrooms are shared. There is an outside deck at the front of the boat where you will be served tea and biscuits, and there are Western and Bangladeshi meals available in the dining room.
Air: There are two domestic airlines--Government-owned Biman and privately owned GMG. Biman has the larger planes, but GMG is classier. Most routes are between Dhaka and regional cities. The Dhaka-Chittagong service is the most popular, taking about 50 minutes and costing around US$50. Other services operate to Barisal, Jessore, Rajshahi, Sylhet, Cox’s Bazar, and Saidpur.