There is no direct connection from Mumbai to Tibet. However, you can take the train to Mumbai airport, fly to Lhasa, then take the drive to Tibet. Alternatively, you can drive from Mumbai to Tibet in around 2 days 5 h.
How to get from Mumbai to Tibet
From Elphinstone Rd train to Mumbai airport, fly to Lhasa airport, then drive to Tibet. 23 h 45 min $435. From Mumbai drive to Tibet. 2 days 5 h $397.