In this paper, we argue that the French philosopher Henri Bergson was a hidden interlocutor in Susan Stebbing's critique of Arthur Eddington in her Philosophy and the Physicists. First, we outline Stebbing's critique of Eddington's philosophical-physical writings with a particular emphasis on her case against Eddington's account of the passage of time. Second, we provide evidence that Eddington's philosophy is, at its core, Bergsonian and make the case that Eddington was directly influenced by Bergson's philosophy of la durée. Third, we lay out Stebbing's critique of Bergsonism in her Pragmatism and French Voluntarism and identify important similarities with her critique of Eddington over twenty years later. In doing so, we show that it is Eddington's Bergsonism that she is attacking. Finally, we situate Stebbing's criticisms of both Eddington and Bergson within two wider conflicts that emerged in early twentieth century British philosophy: one between an objectively describable time of physics and subjective temporal experience, and the other between science and intuition.