Strut, swagger, bristle, bridle can all mean to assume an air of dignity or importance.
Strut implies a pompous or theatrical affectation of dignity, especially as shown in one’s gait or by one’s bearing in movement.
Swagger implies ostentation, a conviction of one’s superiority, and, often, an insolent or overbearing gait or manner.
Bristle implies an aggressive manifestation sometimes of anger or of zeal but often of an emotion or desire that causes one to display conspicuously one’s sense of dignity or importance.
Bridle usually suggests awareness of a threat to one’s dignity or state and a reaction (as of hostility, protest, scorn, or resentment) typically expressed by a lofty manner with a tossing up of one’s head and a drawing in of one’s chin.