My hotel is in Colaba near the Gateway of India. I like to know what's the cheapest way to get to the international airport by 8am.
The cheapest way to get around will be to take a B.E.S.T. bus from Colaba to the international airport (called Sahar, or CST). Unfortunately, there is no direct route, and the schedules for the buses are not followed strictly, for you to workout the connections.
Another way would be the local trains, but again, in the absence of anything direct, there would be changes involved.
Based on the fickleness of Mumbai traffic, and the urgency surrounding a trip to the airport, I would recommend flagging down a metered taxi around 5.30 am. The journey, theoretically, is only about 30 km, but traffic can get gnarly. The cost should be less than US$15, in INR, of course.
Additionally, if you are getting late, you may want to consider asking the taxi to take the Bandra-Worli sealink. This does carry a toll, and use only if you are short on time.
Here's what I ended up doing:
I left my hotel at 5:30 to walk up to Colaba Causeway to catch a bus to Churchgate station. There are at least four different buses doing this route including the 106,123 and 132. I had to wait 30 minutes for the first bus, in this time I could have walked to the station. The fare was 6 Rs.
At Churchgate I bought a ticket (8 Rs) for the fast train to Andheri station which left at 6:14 and took about 35min. There are many trains but I recommend using a fast one.
Because I was good on time, I had breakfast at a restaurant near Andheri station for 20 min and then took bus No.308 (7 Rs) right to the airport. Finally there was a 3min walk to the terminal. So the whole journey took less than 2 hours and cost 21 Rs (US$0.42).
If you are leaving later in the day, the traffic is much havier but there are also more frequent buses. Also both buses and trains get very busy during rush hour, but I still think it is possible to do this at any time of the day if you don't have too much luggage.