I had traveled to Bangladesh in 2006 and stayed with my mother's family in the Lalbagh area of Dhaka, which is considered the "old town" and is at the southern end of the city. I was accosted by a few porters at the airport and out of the blue, they asked I could give them money (described as goosh per vernacular). I knew that it would happen and I just ignored them and they did not bother me afterwards. They had thought that I was from the Emirates or Saudi Arabia, and I was hoping that they would guess that I was an American. Though on the day of our departure, my mother and I had to appease the baggage screener to get into the airport.
Political strife and sometimes violent demonstrations are expected. The rampant cronyism amongst the politicians and prominent business officials stymies progress of improving major infrastructure. Since I was not born in Bangladesh, I would say that I was put off by the apparent adoption of some distasteful elements of Western culture. Yes, I do exhibit characteristics of a fasiq (one who neglects or disobeys Allah's commandments) but understand that the invasive nature of consumerist pop culture or so called globalization, broadly propagated by multinational American and European corporations, will eventually overshadow a third world country's culture (well not all of it). Not that I'm suggesting that your daughter is an agent of said paradigm but she will probably notice it if she observes from an anthropological/sociological perspective. I'll just stop right there and just get on with providing you some of my insights.
Heavy congestion on Dhaka's roads, especially if you're going to the shopping districts, is commonplace and it did put me to sleep a couple times when I traveled by car (probably due to the heat). I preferred rickshaws over cars and 'baby' taxis (look similar to a Reliant Robin). Northern Dhaka, let's say Gulshan and beyond, is a bit more modern yet the development is extremely mismanaged by city officials. However, I did enjoy the unique ice coffee at the bowling alley in Rifle Square. As for eateries, there are some ethnic restaurants in Gulshan near the consulates but they are quite expensive. Apparently the American restaurant where I had dined catered local organic beef steaks. Very rarely did I eat out. Oh, there is a Moghul-era fort in Lalbagh that has some interesting exhibitions.
I do not remember if I had seen any Caucasians during my stay in Dhaka but I'm sure they frequent around somewhere other than Gulshan. There are pale-skinned Bengalis (well not too many) and your daughter should not encounter any trouble. But it doesn't hurt to travel with a trustworthy guide and I would recommend that she wear the local clothing. I don't know if young Bengali men act strange when they spot a Caucasian female but I have heard of a female Peace Corp member being assaulted somewhere in the slums of Dhaka. She should also be cautious when she goes to Cox Bazar. Believe it or not, university campuses in the U.S. have had reported similar cases of assault.
I hope that I didn't cloud your perception of Bangladesh as unapproachable and it was not my intention to do so. I wish your daughter the best in her travels.