Wow ! I really wish I could come with you on this one.
There are direct trains but no direct flights for this journey. Mumbai (Maharashtra) to Rishikesh (Uttarakhand) distance is 1659 km and you can get there by flight + train in just over 8 hours and 17 minutes or by train fares starting from ₹ 536.
It's gonna be warm and sunny, and did I mention warm ?