It was for optional origin wheat possibly from either Russia, the United States or Canada, traders said.
The price includes shipping, insurance and ship unloading costs.
Three other offers were submitted in the tender all on the same C&F liner out terms. Trading house Aston offered $296.49 a tonne for Russian wheat, the sources said.
J.K. International offered $297.10 a tonne for wheat from any origin apart from Israel.
Trading house Swiss Singapore Overseas Enterprises offered $299.04 for Russian, Ukrainian or German wheat.
All the offers were for the full 50,000 tonnes.
Wheat with 12.5 percent protein content was sought for shipment 40 days after contract signing, traders said. The tender had sought wheat from any source apart from Israel.
A report from the United Nation's Food and Agriculture Organisation (FAO) in December estimated Bangladesh's wheat import requirements in the current 2018/19 season at a record of around 6 million tonnes. This would be 34 percent above the previous five-year average following steady increases since 2012/13.
The strong demand for wheat reflects a shift in consumers' diet preferences towards bread as well as the increased use of wheat as a substitute for more expensive rice, the FAO said.
But Bangladesh made no purchase in its previous international tender to import 50,000 tonnes of wheat as the lowest bidder did not agree to a time extension amid rising global prices, the state grains agency said on Feb 4.
Swiss Singapore Overseas made the lowest offer of $290.94 per tonne, CIF liner out, in the previous tender.