There are total 5 trains going to Bhuj from Ahmedabad. You can check the IRCTC website and get to know about it. Also, if possible, get the tickets, please go in Bandra-Bhuj Express. The train is superfast and tops in every other aspects too.I would really recommend you to avoid general and sleeper coach.
Otherwise, there is a good frequency of private Volvo buses going to Bhuj from Ahmedabad. You can check it here.
From Bhuj, the most convenient way is to hire a taxi and go to the Rann of Kutch. That is the best way for safer and comfort ride.
Note – Bhuj is the district capital of Kutch.