The interactions between air bubbles and hydrophobic polymer surfaces in aqueous media play important roles in many industrial and engineering processes. In this work, the interaction forces between air bubble and a model hydrophobic polymer-polystyrene (PS) in NaCl solutions (1 mM to 1000 mM) were directly measured using a bubble probe atomic force microscope (AFM) technique, and the measured forces were analyzed by a theoretical model based on Reynolds lubrication theory and augmented Young-Laplace equation including the influence of disjoining pressure. It was found that the theoretical analysis, by assuming that the PS surface was a pristine and bare polymer surface in aqueous solutions, could not fully agree with the experimental force measurements at intermedium salinity condition (i.e., 100 mM NaCl), and the discrepancy could not be described by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory even including the effects of non-DLVO interactions such as hydrophobic interaction. Atomic force microscope (AFM) imaging demonstrated that the above discrepancy was caused by the presence of interfacial nanobubbles (INBs) on the hydrophobic PS surface. The solution salinity was found to significantly affect the size and surface coverage of INBs on the PS surface, thereby influencing the surface forces. At high NaCl concentration (e.g., 500 and 1000 mM), the INB formation (and its impact on the surface interactions) and electric double layer repulsion were highly suppressed, and the bubble-PS attachment was observed attributing to their hydrophobic attraction with a decay length of similar to 0.75 +/- 0.05 nm. The results agree with our previous surface force measurements between two PS surfaces using a surface forces apparatus. This work provides useful insights into the interaction mechanism between air bubbles and hydrophobic polymer surfaces, as well as the influence of solution salinity and interfacial nanobubbles on the bubble-polymer interaction.