We present multi-epoch, diffraction-limited images of the nebula around the carbon star CIT 6 at 2.2 microns and 3.1 microns from aperture masking on the Keck-I telescope. The near-IR nebula is resolved into two main components, an elongated, bright feature showing time-variable asymmetry and a fainter component about 60 milliarcseconds away with a cooler color temperature. These images were precisely registered (~35 milliarcseconds) with respect to recent visible images from the Hubble Space Telescope (Trammell et al. 2000), which showed a bipolar structure in scattered light. The dominant near-IR feature is associated with the northern lobe of this scattering nebula, and the multi-wavelength dataset can be understood in terms of a bipolar dust shell around CIT 6. Variability of the near-IR morphology is qualitatively consistent with previously observed changes in red polarization, caused by varying illumination geometry due to non-uniform dust production. The blue emission morphology and polarization properties can not be explained by the above model alone, but require the presence of a wide binary companion in the vicinity of the southern polar lobe. The physical mechanisms responsible for the breaking of spherical symmetry around extreme carbon stars, such as CIT 6 and IRC+10216, remain uncertain.