What is the safest, cheapest legal way to send money to Bangladesh from Qatar?

Use a licensed exchange house, not hundi. Hundi is illegal and you can lose your money with no help. Licensed exchange houses in Qatar include Al Fardan Exchange, City Exchange and Doha Bank services; they give a receipt. You need your QID to send money. The Bangladesh government adds a 2.5% cash incentive on money sent through legal bank channels, paid to your family in Taka. On BDT 100,000 they receive an extra BDT 2,500. For amounts over BDT 500,000 your family must show documents. Keep your receipt and compare the rate and fee before you send.