There are two possibilities here.
I was standing in my kitchen. I looked over at the sink.
The familiar context of a (typical modern) kitchen with one sink causes the speaker to use the definite article; the speaker doesn't stop to question the notion that a kitchen has but one sink. It's almost automatic for the speaker to use "the".
If the speaker is standing in the bedroom of a person who does not share the room with another sibling, it would be natural to say "under the bed" as there is only one bed in such a room.
The second explanation: "to run under the bed" is a collocation which means "to run under and cower beneath a bed".
My dog is afraid of fire engines. Whenever he hears one, he runs under the bed.
It might be the same bed, or any bed in the house. The speaker does not care, for the speaker is not referring to a particular bed. The speaker is referring to the act of hiding under a bed in fright.
P.S. In English-speaking countries beds are frequently on a raised platform on four legs, with a small space between the mattress support and the floor below.