The best possible way to reach chitkul is by train+cab.
To reach Chitkul from mumbai you have to take a train to Medak, which is hardly 16hours tour, from Medak you can take public transport or your own personal cab to reach chitkul which is at 5 hours distance from each other.
I took my best way via shimala...
from shimala I took early morning jeep which was sharing and newspaper distributor towards sangla valley... I reached karcham by afternoon. then I took a public bus transport ( hrtc) towards sangla. again I took public bus transport from sangla to chitkul. my route was - shimala - karcham - sangla - chitkul
if you want decent journey you can hire a cab but trust me hrtc bus drivers are super amazing they give you the best rides, being there with public transport is adventure.
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