First of all you have to come first Delhi, Chandigarh, Kalka by Flight and Train from Mumbai. How to reach shimla this is the first quotation which come in the mind. Normally there is lot of way to come Shimla mostly Chandigarh and Delhi is the most preferred location for that.
There is lot of bus services from Chandigarh/Delhi. You can take buses from sector 43. In every 15 Minuit there is bus to Shimla. There is lot of buses are available from morning 5 am to evening 10 pm after then some selected buses are available. Volvo and Deluxe buses timing you can check HRTC website.
you can also take the train from Kalka to Shimla this is the only way to come Shimla by train. it will take 6 hours to reach. There is some selected train from Kalka to Shimla. Toy train Timing you can check IRCTC website
Direct taxi you can take from Chandigarh/delhi airport. You can also take the cab for the full tour covering shimla and manali. The pricing of the cab very according to the no. of days and which cab you will prefer.
from Delhi to Shimla flight is also available which will starts from Delhi Airport in Morning 7 Am and same flight goes back Shimla to Delhi on 8:15 Am. There is only one flight from Delhi to Shimla and only one helicopter services from Chandigarh to Shimla.