If you’re staying in Dhaka for a short period of time — a hotel is going to be your best option. Airbnb is available in Dhaka and is slowly gaining popularity. As of 29th March 2018, there are 400+ homes available for rent on Airbnb in Dhaka. Some really good rooms are available at $10 to $15 per night and it might be your cheapest stay yet.
Hotel wise, most decent option will cost quite a bit of money. Any decent hotel worth staying in will be at least $50 per night, not to mention the best hotels such as Westin and Sheraton will $100+ per night. Your best bet for hotel options is TripAdvisor for Dhaka.
If you’re staying more long-term, it would make sense to rent an apartment in Dhaka. A website that is very useful but underutilized is Bikroy.com, it is a lot like eBay except more evolved and tailored for the Bangladeshi market. You can buy and sell almost anything. You can rent rooms on Bikroy for as low as $100/month — that’s the same price as a one night stay at a fiver star hotel in Dhaka!
Facebook is very popular in Bangladesh and is probably the most accessed service on the internet. There are groups where you can find rooms and apartments available for rent. There’s a Facebook group for almost everything in Bangladesh.