If you are flying B/F, you clearly have a little cash to splash.

Just take a free shuttle or taxi to a 5-star airport near the hotel, and ask the bellhop to check your bags while you go in for lunch. After lunch, go spend the afternoon touring Bombay, and come back in the evening and collect your bags...

Or simply hire a car for the day, which can be done for $30-$80, depending on how hard you look. Keep the bags in the trunk.

Theft is (in my experience, having spend maybe 16 months in bombay over the past seven years) surprisingly rare....

Shawn