According to this:
http://bdlaws.minlaw.gov.bd/act-242/section-7472.html
"5. Subject to the provisions of section 3 a person born after the commencement of this Act, shall be a citizen of Bangladesh by descent if his 1[father or mother] is a citizen of Bangladesh at the time of his birth:
Provided that if the 2[father or mother] of such person is a citizen of Bangladesh by descent only, that person shall not be a citizen of Bangladesh by virtue of this section unless-
(a) that person's birth having occurred in a country outside Bangladesh the birth is registered at a Bangladesh Consulate or Mission in that country, or where there is no Bangladesh Consulate or Mission in that country at the prescribed Consulate or Mission or at a Bangladesh Consulate or Mission in the country nearest to that country; or
(b) that person's 3[father or mother] is, at the time of the birth, in the service of any Government in Bangladesh."
And according to this:
https://www.360lawservices.com/immi...-shamima-begum-and-the-new-precedent-it-sets/
"In the case of UK citizens of Bangladeshi heritage like Shamima Begum, Bangladeshi national law states that citizenship is given automatically at birth through bloodline (jus sanguinis), giving them dual nationality.
Unless they make an active effort to retain it, however, their Bangladeshi citizenship effectively becomes dormant at the age of 21. As it is thought that Shamima’s mother is Bangladeshi and Ms Begum is still currently under the age of 21, the Home Office can somewhat justify their decision and gain reassurance there was a legal basis for stripping Ms Begum of her UK citizenship."
It seems she is entitled to Bangladeshi citizenship and legally the UK has done nothing wrong.