There are lots of people asking this, so I assume quite a few languages use an "on" sort of word for this case, but English doesn't usually.
You're right about using "on" when A is on top of B, but for sleeping in bed, one is usually under the covers, so the normal way to say it is "in the bed". One might fall asleep on the psychiatrist's couch, though, since there are no covers.
I don't think "on the bed" is really wrong, but it doesn't sound natural. I also think the Spanish word "en" naturally translates to the English word "in".
There is nothing wrong with the English translation. "On the bed", "in the bed", or "in bed" all depend on the position of the person.
"On the bed" means that the person is either sitting or lying on the blanket.
"In the bed" means that the person is under the blanket
"In bed" means the same thing as "in the bed", but there are some times where one is favoured over the other. For example, I would say "I am in bed" and not "I am in the bed" (unless I was referring to a specific bed).
Because of this, context is probably the most important part of language. Without it, words and sentences are meaningless.
Hth and I think they need to be able to get Henry today? I should be there in a minute. I don't even know the details yet but he'll be home soon or should I be prepared to go get Henry? I should be making jam but in I'm not sure it's daddy's s night to put you to bed yet but he'll be home soon or should I be prepared to go get Henry? I should be making jam but in I'm not sure it's daddy's s night to put you to bed yet but he'll be home soon or should I be prepared to go get Henry instead of going to the meeting just in case you have brilliant answers to the gym I really don't have much in the way to Drogheda so Ted can feed you want to. The only thing I did was the day? How are you doing? :-)