From Mumbai, You can go to multiple destinations to reach Rishikesh. Mumbai to Delhi then Rishikesh
Via Flight
Take a flight to Delhi (2500 -3000 rupees) which will take 2 hours approx then take a Volvo bus to Rishikesh(600 -700 rupees) which will again take 6 hours approximately. Mumbai to Haridwar then Rishikesh
Via Train
It is the most convenient way to reach Rishikesh but it will take time around 18–24 hours to reach there. Take a direct train to Haridwar from Mumbai which can cost around 800–4500 depending on which class you are traveling.
sleeper class will cost you around 800–900 rupees
3rd AC will cost you around 1500–2800 rupees
2nd AC will cost around 2800–3500 rupees
1st AC will cost you around 3500 4500 rupees.
From there you can take a local bus or taxi to Rishikesh which will not cost you more than 100 rupees and take almost 45 minutes. Mumbai to Dehradun then Rishikesh
Via Flight
Take a flight to Dehradun which may cost you from 3700 to 7000. but it will take approx 3 to 5 hours depending on a flight is connecting or direct.
Then take a Bus or taxi to Rishikesh which will take around 30 minutes to 1 hour to reach Rishikesh and cost you 40 to 100 rupees. Good Luck!!!
Happy Travelling!!!