She walks toward you, stops, dips her whole front end in a deep bow, and coos as she rises, then does it again. To a person who has never lived with a pigeon, the performance can look like a threat display or a strange malfunction.
The bow-coo is a named display in pigeon behavior: the bird bows forward, inflates her throat so the coo resonates, and rises again, often circling or fanning her tail as the sequence repeats. Pigeons direct it at birds they are bonded to, as greeting, as courtship, and as a way of holding a relationship in good repair. A pet pigeon who aims it at family members has simply included the humans in the category the display was built for. You are not her audience. You are her flock.
A Display Aimed at Flock, Not Strangers
Context proves the reading. She does not bow-coo at the window, at visitors she has just met, or at objects. She aims it at the particular people who feed her, handle her, and share her room, and often at one favorite person most of all. That targeting is the signature of a bonded display: it is addressed, personal, and repeated to the same recipients day after day, the way a greeting between family members is.
Courtship coloring can come with it, and that is normal too. A bonded hen may bow-coo as part of treating a favored human as mate-level important, alongside following that person around, cooing from a chosen perch when they leave, and presenting herself proudly when they return. None of that needs correcting or discouraging. It is the social system of a flock animal working exactly as designed, in a home where the flock happens to walk on two legs and only one member has feathers.
Not Aggression, Not Distress
The display is easy to misread because the bow brings her head low and the coo can sound insistent, but the rest of her body separates greeting from trouble. A displaying pigeon stays loose and forward-moving: she approaches voluntarily, her feathers lie in their normal position, and she repeats the display in a rhythm, pausing to look up at her person between bows. Aggression in a pigeon looks different, with wing slaps, pecking lunges, and a bird driving another bird or a hand away from a nest or perch.
Distress separates itself just as clearly. A frightened or unwell pigeon goes quiet, fluffed, and withdrawn, or flutters in panic away from contact; she does not walk toward a person and perform a formal greeting at them. Reading the bow-coo correctly protects the relationship in both directions: nobody flinches away from a compliment, and nobody mistakes a social bird's finest gesture for a problem to be trained out of her.
Answering in Kind With Calm Presence
You cannot bow-coo back, and she does not need you to. Answer in kind with the pigeon version of politeness: calm presence. Stay where you are, let her approach and finish the display, talk to her softly, and offer a slow hand for a step-up or a gentle stroke if she usually enjoys one. Rushing toward her, grabbing at her mid-bow, or laughing loudly over the display all swamp a quiet social moment with human-scale energy, and a bird whose greeting keeps getting swamped may stop offering it.
Feed her social nature the rest of the day too. Pigeons are flock animals in their routines as well as their displays: company during cage cleaning, a place near household activity rather than in an isolated room, and unhurried time out of the cage near her people all tell her the flock bond runs both ways. If she directs the display mostly at one person, let that person enjoy the honor, and let others build their share through feeding and quiet company rather than competing for her attention. Her care is flock work in this house, and KinsLe keeps it that way through Care Teams, where the person she follows most can still hand a feeding turn to someone else.