Bismillah Airlines does exist, and as far as their operations, they have been operating short-term leased aircraft which have included an L1011 and AN
Bismillah is a division of the Mollah Group -- which itself is a large export-import company and thus has vested interests in air cargo in Bangladesh. Currently, one of the projects Bismillah has undertaken is to ferry shrimps from Cox's Bazar to Jessore via Chittagong in Bangladesh. All of Bismillah's aircraft seem to be short term dry lease and the only identifying marks on the aircraft are a small label stuck on the fuselage.
As far as I know, Air Bangladesh and Bismillah are not related, but then again, who knows in the intricate affairs of Bangladeshi business folks. Air Bangladesh, as reported, ran intro trouble 2 years ago with hajj operations, but I suppose they have now sorted out enough of their problems to lease a B747.
Cargo demands in Bangladesh are rising much faster than passenger volume, and I am not surprised to see more than one entrant in the market -- especially since Biman has no dedicated freighters.
Wasim / Planemannyc