Both "in" and "on" are possible.

When you are under the covers, you're "in bed". When you are shown to a bedroom where you will be spending the night, you're shown the bed you will "lie on" or "sleep on" or "sleep in".

I would choose "on" if I were shown to a cot, not a full bed.

The hotel room was small and since there were five of us, we had to sleep on cots.

So "on" could imply a something like a cot.

Most Americans, I think, would also use "on" if complaining about the mattress or thinking of the bed in terms of its mattress. Some mattresses look as though they will deliver an unpleasant night's sleep.

I'd like to speak to the manager! This room was quite expensive, and yet the mattress was terribly uncomfortable. The springs were poking me and I couldn't get to sleep on that old bed!

Both "in" and "on" are possible.

When you are under the covers, you're "in bed". When you are shown to a bedroom where you will be spending the night, you're shown the bed you will "lie on" or "sleep on" or "sleep in".

I would choose "on" if I were shown to a cot, not a full bed.

The hotel room was small and since there were five of us, we had to sleep on cots.

So "on" could imply something like a cot.

Most Americans, I think, would also use "on" if complaining about the mattress or thinking of the bed in terms of its mattress. Some mattresses look as though they will deliver an unpleasant night's sleep.

I'd like to speak to the manager! This room was quite expensive, and yet the mattress was terribly uncomfortable. The springs were poking me and I couldn't get to sleep on that old bed!