Hi JimJams,
If you currently hold a UK passport, then it would mean that you are a UK citizen. Otherwise, you would still be using your Bangladesh passport. It is likely that you were naturalized unless all children born to UK citizens automatically become UK citizens no matter what country the child was born? According to the link below, dual citizenship is not recognized in Bangladesh. Contact your local Bangladesh embassy for clarification.
There are other country passports that do not require a visa to enter Bangladesh. So in your situation, this does not necessarily mean you still have Bangladesh citizenship.
Check out the following links that I found in regards to US and Bangladesh relations. The FAQs 2nd link should be applicable to anyone.
Dual Nationality
http://www.bdcgny.org/dual_nationality/dnc_frequently_asked_questions.pdf
If you currently hold a UK passport, then it would mean that you are a UK citizen. Otherwise, you would still be using your Bangladesh passport. It is likely that you were naturalized unless all children born to UK citizens automatically become UK citizens no matter what country the child was born? According to the link below, dual citizenship is not recognized in Bangladesh. Contact your local Bangladesh embassy for clarification.
There are other country passports that do not require a visa to enter Bangladesh. So in your situation, this does not necessarily mean you still have Bangladesh citizenship.
Check out the following links that I found in regards to US and Bangladesh relations. The FAQs 2nd link should be applicable to anyone.
Dual Nationality
http://www.bdcgny.org/dual_nationality/dnc_frequently_asked_questions.pdf