We have studied the cosmological motion of a sample of 40 supernovae (SNe) type Ia, whose distances have been carefully determined, and corrected for reddening. The redshifts of the sample range from 3000-30,000 km/sec. Our best estimates show that the bulk of the SN Ia are at rest in the frame defined by the cosmic background radiation; i.e., the reflex motion of the Milky Way in the SN frame reproduces the CMB dipole with significant accuracy. The bulk flows in this frame are typically 200+/-200 km/sec. Most of the signal comes from the sample between 3000 and 15,000 km/sec. At higher redshifts the precision of the SN Ia distances (typically 10%) are insufficient to detect typical peculiar motions (our signal becomes dominated by noise). The "convergence depth" and scale of these motions appears to be about 10,000 km/sec. These results are at variance with the large bulk motions measured by Lauer and Postman (1994) and Hudson et al (1999). Our motions and scale appear to be consistent with cosmological simulations of CDM, which predict the gravitational accelerations of typical observers given the expected distribution of matter in the universe, when scaled by the abundance of rich clusters.