You can take a train/ flight from Mumbai to Delhi, you can check for train bookings on IRCTC. And from Delhi, Kashmere Gate there are HRTC buses to Dharamshala, and from Dharamshala there are ordinary buses to Dalhousie too.
Hey Nikhil, Take a direct train from Mumbai to Pathankot or Mumbai to Delhi then from Delhi to Pathankot. From Pathankot, take a state transport bus to Dharamshala ( 4 hours ). Then spend at least 3-4 days there ( Book hotels in Bhagsu or Dharamkot ). Then from Dharamshala tak a bus or cab to Dalhousie and spend at least 2 days there. This is my itinerary of Dharamshala which would help you : https://www.tripoto.com/trip/four-day-itinerary-of-dharamshala-5bbf6eb477505?ref=mobwapp&source=awp Places to visit in Dalhousie : 1)St. Patrick's Church 2)Subhash Baoli 3)Bara Pathar Temple 4)Chamba 5)Khajjiar 6)Laxmi Narayan Temple 7)St. John's church 8)Norwood Paramdham for sunset Happy travelling!!!!!
If you are traveling alone I suggest you to use Himachal roadways buses. As HRTC (HIMACHAL ROAD TRANSPORT CORPORATION) provides best budget transportation facilities as compare to hire a Pvt. taxi and the frequency is not bad for various station. you only need to check the time table of the buses. HRTC has its official site for online booking you can google it and remember you have to make your login account first on hrtc booking site. You can book Volvo or Isuzu buses directly to Dharamshala through the site as well as normal buses also and if you are going Dhalhousi first you have to book bus upto Chamba then you have to catch a local or hrtc bus for Dhalhousi depend on your choice. Dhalhousi and Dharamshala both are connected with state bus route so you don't need to worry travel inside the state you will get any bus between these station. Remember advance booking depends on ur choice or you can directly catch a bus from ISBT KASHMIRI GATE DELHI at night. Mostly hrtc buses depart at night from Delhi upto at 10 pm. so be on time there