How to get from Nara to Uji

How long does it take to travel from Nara to Uji by JR from JR Nara Station. Also, is their a bus worth taking?, I will be in Nara for seven Days and want to do some interesting day trips before going to Kyoto for five days. Any suggestions would be welcome. Thank you.

How long does it take to travel from Nara to Uji by JR from JR Nara Station.

30 minute by rapid train or 40-45 minutes by local train:
http://www.hyperdia.com/

Also, is their a bus worth taking?

No.

I will be in Nara for seven Days

Wow, that is a very long stay! I hope you are interested in Japanese history! My recommended trips besides Nara and Horyuji are Asuka, Hasedera, Muroji Temple, Yoshino and Iga Ueno:
http://www.japan-guide.com/list/e1105.html

When will you be in Nara?

As Uji mentioned, Yoshino is also recommended. Yoshino mountain is absolutely stunning in spring!

I will be in Nara from 20th Nov. till 27th Nov., Autumn peak period, then onto Kyoto for five nights, this is because I could not get good accommodation in Kyoto before the 27th., already heavily booked!. Using Nara as my base for seven days is ok with me, staying at the Super hotel at JRNara station area and will bean opportunity to do some full day trips from Nara before going to Kyoto for my main stay. .

Uji that time of year is spectacular with the autumn leaves! you are really lucky. It will be bitterly cold though (highs probably under 10 Celsius, and I think it was below zero when we were out walking early in the morning there). No matter how cold, have a green tea icrecream because they taste better there than anywhere else, IMO. Uji is a really lovely little town.