If I were you, I´d probably send from Malaysia, Port Klang by sea or Kuala Lumpur (KLIA) airport by air, to save the hassle of getting the bike to Singapore. Theres a top-condition motorway between all these, so they are only 4-5 hours apart.
We sent from Chennai to Bangkok (via KLIA) by Malaysia Airlines, the cargo agent in India was Shell Air, but I dont have the contact details right here, I can look them up, though (I should post them to the shipping pages, too). They handled the job fine, but I dont know, if they would be able to help you from the other end, might be worth asking, though. Cost something like 550-600 euros total to fly the bike to Bangkok.
I also met a German biker in Malaysia, who had been asking about shipping from there to India... and I think I wrote down the details, including the agent he was planning to use. I can check, if I still have these (but I havent used them, and neither had the German guy then, so I cant recommend them to you).
Last January, there was some sort of wrestling with the union going on at Chennai port, which meant that cargo moved very slowly thru there. Thats why we opted for air. I dont know, if the situation there is now better.
Some of the quotes I got for seafreight between India and Malaysia were almost as much as flying, but I think you should be able to get it done by sea considerably cheaper than airplane, you just have to find the right contacts.