Any time is ohk.. but December to March will be Soo cold that it's very hard to complete.. try out in April to may range.. so that you will reach north by the time the climate is perfect
HI Pradeep,
I think you may start in the mid of March or April. Please ensure to reach max by Mid-May, Monsoon will start in the end of may. Taking a bike will be a problem in that case as the distance planned is very long.
During winter and rainy it would be difficult and dangerous to complete the bike trip from Kannyakumari to Kashmir. Best time for this trip would be from April to May as weather will be pleasant and roads will not be blocked.