December to march is good. You could rent the bike in India with less hassles...but i think only enfield or "Oilfield"...
will be available easily everywhere for rent. But this also depends on how long you want to ride in India.
Personally if i travel to north india...i either fly or take the train. and then locally hire a bike for a week or few days and ride it. done this only in Rishikesh and Pushkar till now....but was a good experience..
and if you are anyhow taking your bike and want to stop by in India..the months mentioned are good...even november will be ok..
if you can bear the heat and some rain anytime in the year is fine...you see, considerable part of india moves on two wheels