Bangkok and Calcutta are the main destinations for flights in and out of Bangladesh. Overland routes between the subcontinent and Myanmar have been closed since the early 1950s. Even if the border was to be opened in the future, it's likely that all the formerly navigable roads across the frontier have long since been devoured by the jungle. Transportation Internal transport in Bangladesh is cheap. Biman, the national carrier, has flights radiating from Dhaka to 10 Bangladeshi cities, including Chittagong and Cox's Bazar.
Flights are cheap but are still more than three times first class train fares.
Bangladesh has a fairly extensive system of passable roads but they are chokka with buses. Bus drivers in Bangladesh are among the world's most reckless, as evidenced by the incredible number of bus accidents occurring every day. Trains are a lot easier on the nerves, knees and backside, and those plying the major routes are actually quite good, at least in first class. A trip to Bangladesh which does not include taking a trip down a river is like going to the Alps and not skiing or hiking. The famous 'Rocket' paddlewheel steamer runs from Dhaka to Khulna four times a week, but there are plenty of other fascinating ferries to catch.