I spent 3 months cycling in southwest India earlier this year and yes it is insanity but of the most memorable type so go for it. I started in Goa and cycled down the coast as far as Mangalore then up into the western Ghats to Madikeri. From there to Ooty, I did push up the last part of the hill, and down the other side, over 1,000 metres of drop in 12 miles along fabulous mountain road, to Fort Cochin. from there I carried on down to Trivandrum before getting the train back to Goa.
I spent about half the time relaxing on the beach or at a hill station so this entire route is possible in 6 weeks but would suggest if you did take it limiting it to no further than Fort cochin.
Cycling can be challenging, be prepared to bail off the road if you think you are about to be run over, no need for camping gear, hotels are close enough together, look out for signs saying lodge, a hotel might only be a restaurant, it is usually ok to take your bikes into your room, if not there is always somewhere safe to put them.
It is no longer easy to take a bike on a bus but the train is no problem, go to the goods office and in an emergency flag down a lorry and offer them some money to take you somewhere. Roadside food is readily available and good, bottled water can be had anywhere.
Emirates and Gulf airlines give 30 and 28 kg luggage allowance so taking your bikes cost nothing, get cardboard boxes from a bike shop. If you want to buy there reasonable 18 speed mountain bikes are available for about £100 but they are quite heavy, atms in all towns take visa and mastercard.
Any more questions you can pm me.
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