The domestic BOM-HYD flight departs from a different airport terminal, which is a 15-20 minute taxi ride away. Baggage must pass through customs and immigration at BOM when connecting to 9W.

When flying BOM-HYD-BOM, Air India 050 and 051 continue to international destinations, so you can tag bags through to/from HYD and not have to change airport terminals. Which is a massive help, because the 2 terminals are basically 2 different airports which share a runway.

Hopping in a taxi/shuttle bus with bags in the middle of the night is not a particularly exciting prospect...