Bent-double radio sources have been used as a probe to measure the density of intergalactic gas in galaxy groups. We carry out a series of high-resolution, 3D simulations of AGN jets moving through an external medium with a constant density in order to develop a general formula for the radius of curvature of the jets, and to determine how accurately the density of the intra-group medium (IGM) can be measured. Our simulations produce curved jets ending in bright radio lobes with an extended trail of low surface brightness radio emission. The radius of curvature of the jets varies with time by only about 25%. The radio trail seen in our simulations is typically not detected in known sources, but may be detectable in lower resolution radio observations. The length of this tail can be used to determine the age of the AGN. We also use our simulation data to derive a formula for the kinetic luminosity of observed jets in terms of the radius of curvature and jet pressure. In characterizing how well observations can measure the IGM density, we find that the limited resolution of typical radio observations leads to a systematic under-estimate of the density of about 50%. The unknown angles between the observer and the direction of jet propagation and direction of AGN motion through the IGM leads to an uncertainty of about 50% in estimates of the IGM density. Previous conclusions drawn using these sources, indicating that galaxy groups contain significant reservoirs of baryons in their IGM, are still valid when considering this level of uncertainty. In addition, we model the X-ray emission expected from bent-double radio sources. We find that known sources in reasonably dense environments should be detectable in ~100 ks Chandra observations. X-ray observations of these sources would place constraints on the IGM density and AGN velocity that are complementary to radio observations.