Although E.W. Barton-Wright recorded details of the stick fighting and jujutsu aspects of Bartitsu in his Pearson’s Magazine articles, it took many years of painstaking research and educated guesswork to piece together the Bartitsu Club’s take on (kick)boxing. This video is a decent representation of that style, as performed in a friendly, technical sparring match.
In particular, note the aggressive, elbow-forward defences displayed by the fighter in the black and white t-shirt and the transitions from the striking range to the grappling/jujutsu range, both key markers of Bartitsu unarmed combat.