We present a detailed study of the bar fraction in the CfA sample of Seyfert galaxies and in a carefully selected control sample of nonactive galaxies to investigate the relation between the presence of bars and of nuclear activity. To avoid the problems related to bar classification in the Third Reference Catalogue (RC3), e.g., subjectivity, low resolution, and contamination by dust, we have developed an objective bar classification method, which we conservatively apply to our new subarcsecond resolution near-infrared (NIR) imaging data set discussed in the first paper in this series. We are able to use stringent criteria based on radial profiles of ellipticity and major axis position angle to determine the presence of a bar and its axial ratio. Concentrating on noninteracting galaxies in our sample for which morphological information can be obtained, we find that Seyfert hosts are barred more often (79%+/-7.5%) than the nonactive galaxies in our control sample (59%+/-9%), a result which is at the ~2.5 σ significance level. The fraction of nonaxisymmetric hosts becomes even larger when interacting galaxies are taken into account. We discuss the implications of this result for the fueling of central activity by large-scale bars. This paper improves on previous work by means of imaging at higher spatial resolution and by the use of a set of stringent criteria for bar presence and confirms that the use of NIR is superior to optical imaging for detection of bars in disk galaxies.