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

Use a licensed exchange house or bank app, not hundi. Hundi is illegal and gives no protection if the money is lost. Licensed options in Saudi Arabia include Al Rajhi Bank's Tahweel, STC Pay and Enjaz; they give a receipt. You need your Iqama to send money. The Bangladesh government adds a 2.5% cash incentive on money sent through legal channels, paid to your family in Taka. On BDT 100,000 they get an extra BDT 2,500. For amounts over BDT 500,000 documents are needed. Keep every receipt and compare the fee and rate before sending.