Travel to Sri nagar from Jammu and then take a bus from Sri nagar to Leh via Kargil.
It would be a 9+23 hours journey if combined.
Srinagar to Leh by bus
The bus departs at 8 AM from Tourist reception center near Dal Lake. It is a two days journey with night halt at Kargil. The bus stops at all popular tourist places for a little while for sight seeing. It reaches Kargil by evening and starts again the next day early in the morning for Leh; where it arrives by late afternoon or evening.
It would be better if you either take a cab or rent a car and have some friends with you since you can then drive on sharing basis as its a long drive.Alternatively you can go to Leh from Delhi via flight