By the bye is a phrase that is often used to add an additional but less significant thought to a conversation. Antonyms, or words that have the opposite meaning of "by the bye," would be terms that convey a sense of significance or urgency. Examples of antonyms for "by the bye" include "critical," "essential," "important," "major," "paramount," "pressing," and "significant." These words indicate that what is being discussed is of great importance and should not be dismissed or overlooked. Unlike "by the bye," which suggests a casual or incidental comment, these antonyms convey a sense of gravity and importance to the topic being discussed.