To facilitate long-term engagement with social robots, emerging evidence suggests that modelling robots on social animals with whom many people form enduring social bonds-specifically, pet dogs-may be useful. However, scientific understanding of the features of pet dogs that are important for establishing and maintaining social bonds remains limited to broad qualities that are liked, as opposed to specific behaviours. To better understand dog behaviours that are perceived as important for facilitating social bonds between owner and pet, we surveyed current dog owners (n = 153) with open-ended questions about their dogs' behaviours. Thematic analysis identified 7 categories of behaviours perceived as important to human-dog bonding, including: 1) attunement, 2) communication, 3) consistency and predictability, 4) physical affection, 5) positivity and enthusiasm, 6) proximity, and 7) shared activities. We consider the feasibility of translating these behaviours into a social robotic platform, and signpost potential barriers moving forward. In addition to providing insight into important behaviours for human-dog bonding, this work provides a springboard for those hoping to implement dog behaviours into animal-like artificial agents designed for social roles.