Drowning in bathtubs happens. In 2000 in the US there were 341 deaths by drowning and submersion while in or falling into bathtubs. (Data) Though this data doesn't show the age factor.
Most sources, like this one, examine child drowning reasons. And it says that 75% of children who drowned were younger than 24 months.
As for adults, I didn't find any listed causes. But I would say they all happen when a person is unconscious, and there could be many reasons for that: fainting, heart attack, stroke, alcohol/drug poisoning, head injury, etc. Falling asleep is much less likely, as reflexes will kick in, but combined with the factors mentioned above - it's possible.
As personal example: once I fainted because the water in the tub was too hot. It took probably 10-20 seconds until I realized that I was under water and another 20-30 seconds to stand up, because it was slippery and I was drowsy. Of course it wasn't enough to drown, but I can see how it could happen.