The phrase "putting a bug ear" is an interesting idiom which means to suspiciously listen in or eavesdrop on someone's private conversation. If you're looking for synonyms for this phrase, you could use "spying", "overhearing", "monitoring", "snooping", "listening in", or "eavesdropping". These words have been used for a long time to describe the act of secretly gathering information or observing someone without their knowledge. Although it may seem intrusive and unethical, sometimes it's necessary to gain knowledge in certain situations. However, it's always better to ask permission or outrightly reveal your intentions of listening in on someone to avoid causing any trouble.