The interaction between an acoustically driven microbubble and a surface is of interest for a variety of applications, such as ultrasound imaging therapy. Prior investigations have mainly focused on acoustic effects of a rigid boundary, where it was generally observed that the wall increases inertia and reduces the microbubble resonance frequency. Here we investigate the response of a lipid-coated microbubble adherent to a rigid wall. Firm adhesion between the microbubble and a glass surface was achieved through either specific (biotin/avidin) or nonspecific (lipid/glass) interactions. Total internal reflection fluorescence microscopy was used to verify conditions leading to either adhesion or non-adhesion of the bubble to a glass or rigid polymer surface. Individual microbubbles were driven acoustically to sub-nanometer-scale radial oscillations using a photoacoustic technique. Remarkably, adherent microbubbles were shown to have a higher resonance frequency than non-adherent microbubbles resting against the wall. Analysis of the resonance curves indicates that adhesion stiffens the bubble by an apparent increase in the shell elasticity term and decrease in the shell viscosity. Based on these results, we conclude that surface adhesion is dominant over acoustic effects for low-amplitude microbubble oscillations.