Bugeye is a slang term used to describe someone with bulging, wide-set eyes. Although there is no perfect synonym for this word, there are some expressions that may work as alternatives. "Pop-eyed," "bug-eyed," and "goggle-eyed" are some of the words that can describe the same condition. These adjectives focus on the prominent appearance of the person's eyes rather than the size or shape. You can also use more descriptive phrases like "protruding eyes," "wide-eyed," or "saucer-eyed" to depict the same feature. In any case, it's important to use words that are non-offensive and respectful when referring to someone's physical features.