Bobbed the head is a colloquial expression that refers to nodding the head up and down. There are several synonym phrases that can be used in place of "bobbed the head" to express the same action. Some of these synonyms include "nodded vigorously," "bowed the head," "dipped the head," "jerked the head," "wagged the head," and "rocked the head." These alternative phrases provide variety to the text and help to avoid repeated use of the same phrase. Furthermore, using these synonyms can add more descriptive detail to the action and make the writing more engaging for the reader.