Bug-eyed is a popular phrase that is used to describe a person with wide and protruding eyes. However, there are many synonyms that could be used to replace the word 'bug-eyed.' These words include 'goggle-eyed,' 'saucer-eyed,' 'owl-eyed,' 'wide-eyed,' and 'astonished-eyed.' These synonyms all convey a similar meaning and can be used interchangeably, depending on the context of the sentence. For instance, instead of using the phrase 'bug-eyed,' one could say 'she had an astonished-eyed expression.' By using these synonyms, a writer can add variety to their writing and prevent the repetition of the same word, making their work more interesting and engaging.