The phrase "bellied up to" is often used to describe someone who is seated or standing very close to a counter or bar. It is an informal expression and typically denotes a relaxed, casual atmosphere. Some antonyms for "bellied up to" would include "stood back," "kept their distance," or "remained at a distance." These phrases would suggest a more reserved and cautious approach to the situation, as opposed to the bold and confident posture implied by "bellied up to." Other antonyms might include "kept to themselves" or "preferred to observe from afar," which would indicate a preference for privacy and solitude rather than socializing with others.