You could do a loop from Delhi, similar perhaps to the following example.

Start in Delhi, then head to Rishikesh, from Rishikesh, head to Shimla, and from there you can access Spiti Valley, a rough seven or eight days motorbiking through one of the remotest regions in the world. If you survive that and the bike is still in once piece, you should arrive in Manali for repairs, and some relaxation. Once you are ready to go, it is then a 4-5 day journey to Leh. Again this is also very remote but you can count on passing jeeps and trucks to assist you, should you break down. It is wise to plan these trips well, and be prepared for freezing night time temperatures on the passes.

Once you arrive at Leh, use Leh as a base to explore Ladakh. You could easily spend 3-4 weeks in Ladakh, using your bike to get out to visit places like the Nubra Valley, etc. From Leh you can head east; it takes 2-3 days to arrive in Srinagar, if you feel you have still not had enough of remote mountain landscapes, extremely poor roads, etc, think about doing Zanskar, a 5-7 day return trip through the Zanskar range, it is a stunning, remote, beautiful, and very testing journey. People are put off, because you must return the same way you get there; and the 'road' is appalling. One of the biggest draws to go there is that nobody else does.

You access it from a town called Kargil, which is near enough bang in the middle between Srinagar and Leh. Once you arrive in Kashmir, take it easy and enjoy the beautiful scenery. You could easily spend a very relaxed two weeks in Kashmir, check the political situation, respect that fact that Muslims have different ideas about dress code, etc, and you'll find it a hospitable place as anywhere else in India. The only problem with Kashmir is getting out, I did the road a few years ago and you'll be battling with a lot of drunken truck drivers, dozens of military trucks storming past you, and everything in-between.

Some areas are not that friendly to outsiders and things can get out of control quickly because tensions run high along the boarders. You should plan your route well, leave early, and head to a place called Pathenkot*, or something like that, from there it is an easy days ride to Dharamasala, if you still have time left, I'd suggest you go to Delhi via The Punjab, visiting Amirista, break the journey at Chandighar, or even take a detour to Rajasthan, and arrive back at Delhi with enough time to sell/return the bike and spend a few days in Delhi to relax, and visit its many attractions.

Good luck

* there is a bypass road that keeps to the hills. You might want to check this; when I did it, it was said to be in very poor condition and washed out, but maybe they paved it now.