It resembles a double bass, but is more in the shape of an oval rather than having a more straight bottom. The instrument plays in bass clef and is one of the lowest-pitched in the string family.
It closely resembles the cellos that have been illustrated later in the show.
Role in episode
SpongeBob plays a song on the bassinet about him and Squidward's friendship. At one point, when SpongeBob begins one of his lyrics with "Squidward...," Patrick interrupts the song by adding "Likes Patrick more than SpongeBob" to the lyric. This angers SpongeBob so much that he criticizes Patrick in the song and destroys the bassinet.
In real life, a "bassinet" is actually a synonym for a cradle.