The answer is no.
A foreigner cannot buy real property in Bangladesh.
I am not aware of any law which specifically prohibit the buy of land by any foreigner. Also, I am not aware of any law which specifically allow a foreigner to buy land.
Transfer of Property Act 1882 and the Registration Act 1908 are the two main laws which regulate transfer of property in Bangladesh. These two laws do not have any provisions related to foreigner, which may allow a foreigner to buy land in Bangladesh.
Article 13 and 42 of the constitution of Bangladesh speaks about ownership.
13. Principles of ownership:
The people shall own or control the instruments and means of production and distribution, and with this end in view ownership shall assume the following forms –
(a) state ownership, that is ownership by the State on behalf of the people through the creation of an efficient and dynamic nationalised public sector embracing the key sectors of the economy;
(b) co-operative ownership, that is ownership by co-operatives on behalf of their members within such limits as may be prescribed by law; and
(c) private ownership, that is ownership by individuals within such limits as may be prescribed by law.
42. Rights to property
(1) Subject to any restrictions imposed by law, every citizen shall have the right to acquire, hold, transfer or otherwise dispose of property, and no property shall be compulsorily acquired, nationalised or requisitioned save by authority of law.
(2) A law made under clause (1) of this article shall provide for the acquisition, nationalisation or requisition with compensation and shall fix the amount of compensation or specify the principles on which, and the manner in which, the compensation is to be assessed and paid ; but no such law shall be called in question in any court on the ground that any provision of the law in respect of such compensation is not adequate.
As you can see, both articles of the constitution apparently allow only citizen of Bangladesh to own land.
Can a foreigner with work permit buy land in Bangladesh?
The answer is still no. Work permit would not allow a foreigner to buy land.
Is there a way around?
A foreigner can incorporate a company with the Registrar of Joint Stock Companies and Firms. The company would be considered as a local entity and would be able to buy land in its name. Till now, this is the only way a foreigner can buy land in Bangladesh.