Nice ! Looks like you're all set for your vacation ?
There are direct flights but no direct trains for this journey. Bengaluru (Karnataka) to Srinagar (Jammu And Kashmir) distance is 2970 km and you can get there by flight in just over 5 hours and 5 minutes or by train + flight fares starting from ₹ 3458.
It's pleasant weather in daytimes, but can get really cold at nights.