Another possibility is Sri Lanka. The cycling itself isn't as good as Thailand & Laos (road quality varies from good to awful), but it's a fantastic country to visit. Lots of varied sights in a relatively small country. Also some of the most gorgeous beaches in the world. Language is much less of an issue than in Thailand & Laos, as a fair number of people speak English, and road & business signs are often in English. Great food. I haven't been to India yet, but several people who have been to both India & Sri Lanka have told me that: Sri Lanka is cleaner than India; people in Sri Lanka hassle you less than in India; prices are higher in Sri Lanka.
Both Sri Lanka and Thailand have some trains which are fairly bike-friendly. I took a train from Bangkok to near the Lao border with my bike. I also took a couple of trains in Sri Lanka with my bike. The trains there look like they haven't changed in 100 years.