If you are traveling to Kobe from central Kyoto, you might consider taking the private Hankyu Kyoto Line from Kawaramachi or Karasuma Stations. This will get you to Sannomiya Station in roughly 70 minutes or more. You will also have to transfer at Juso Station. The service is slower than taking the JR Kyoto Line but much cheaper at 620 yen. It may also be more convenient as you don’t have to go via Kyoto Station. Remember that the Hankyu Railway is not covered by the Japan Rail Pass.
The alternative route to Kobe is to travel on JR trains via Kyoto Station. The Special Rapid train on the JR Kyoto Line will get you to Sannomiya Station in Kobe in 51 minutes for a fare of 1080 yen. If you have a Japan Rail Pass, you can take a high speed shinkansen to Shin-Kobe Station. This is much faster as it takes only 32 minutes, however Shin-Kobe Station is not as conveniently located as Sannomiya Station.