Hi Rinsha! You are right that the nearest railway station is more than 700km from Leh. In order to reach Leh Ladakh, you have to take taxi/bus service from the railway station and this will take around 15 hours. Both taxis and buses are available near the station. However, the taxi/bus ride from Jammu Tawi to Leh can cost you around Rs 10,000 and the roads ahead are also bumpy. It is better to travel by bus starting from your hometown. Hope this helps!
Govt doesnot run any luxury buses to there it's old school type buses but you will enjoy that too if you can sit on hard seat for continue 12-14 hrs
Rinsha come via Manali
There are two kinds of bus services available: one by the state government and other by private tour operators. Government run buses are a mix of luxury, semi deluxe and ordinary buses. The ones run by private tour operators are usually the semi-deluxe mini buses.
Go via Manali man from Manali it's around 10-12 hrs journey via bus
Reach Jammu by train and than move to Srinagar. In Srinagar you will find many shared taxis and Tempo travellers. I am not sure about Government buses. Other way is Delhi- Leg bus which starts after all the passes in Manali -leh highway. Once you are in LeH there are plenty options if shared vehicles and even Government buses..