If you mean someone is still sleeping or lying there, you would say “in bed.” “She hasn't gotten up yet; she's still in bed.” If you were referring to someone sitting there, you would usually say “on the bed.” “She's sitting on the bed putting on her shoes.”
Why do we say in bed instead of on bed?
We say "in (the) bed" to mean that someone is lying under the bed's covers (such as a sheet and blanket or comforter). Someone under the covers/blankets of a bed is said to be sleeping/lying in (the) bed. They saw Goldilocks sleeping in the bed. He fell asleep as soon as he got in bed.
Why we use in the bed instead on the bed?
the article 'the' suggests that the listener knows which bed is mentioned; or there is only one available bed in which to sleep. The preposition in tells us the person is under the covers, sandwiched between the mattress and the bedsheets.