We use scanning confocal fluorescence microscopy to study the dynamic properties of single fluorescent lipid molecules in unsupported planar bilayers. Specifically, we characterize the emission saturation and diffusive behavior of lipids that have been covalently modified at various locations. By analyzing the time interval between fluorescent bursts, we observe a large deviation from theoretical prediction that indicates a substantial 2D diffusion bias. Interestingly, a correlation between the emission saturation and the power dependency of the deviation suggests that the resonantly enhanced polarizability of the fluorescent label plays a role in the biasing mechanism. Incorporation of the measured fluorescence rate constant into a model for particle escape from a shallow potential well indicates that the well depth is approximate to kT. These results are in agreement with the calculable laser/membrane interaction potential and are consistent with previous reports concerning diffusion biases in free solution caused by weak optical traps.