The attachment of air bubbles to solid surfaces in water is encountered in many natural processes and industrial applications. It has been established that the attachment can occur between hydrophobic surfaces and air bubbles. In this paper, we present novel experimental results to quantify the attachment in terms of the attachment time. We show that the attachment time can be determined from either the transient force curve or the transient film thickness. These techniques for determining the attachment time are based on the fact that the rupture of a thin liquid film produces a large attachment force and a rapid expansion of the three-phase contact radius in comparison with the expansion of the film radius. The experimental results are quantitatively analyzed using thin-film drainage theory and intermolecular forces, which include the advanced multilayer van der Waals force and the electrical double-layer force. The advanced van der Waals force theory allows us to incorporate the effect of interfacial gas enrichment (IGE) of dissolved gas in water at hydrophobic surfaces on the bubble-surface attachment. Critically, if the presence of IGE is ignored, the experimental results do not agree with the theory. Finally, IGE is shown to be a significant factor in controlling hydrophobic attraction between an air bubble and a hydrophobic surface and their attachment.