Traveling from Varanasi to Kathamandu is one of the most popular ways to reach Nepal from India. All options are readily available: bus, train, and plane. Here's an overview of each to help you plan your trip.
Varanasi to Kathmandu Flights
The most convenient way to get from Varanasi to Kathmandu is to fly. It takes approximately an hour. Air India and Jet Airways both operate on that route. Flights cost from around 6,000 rupees ($100) upwards.
Varanasi to Kathmandu Trains
If you're a budget traveler and don't want to fork out for a flight, the next best option is a train and bus combination journey. There's no direct train to Kathmandu, so you'll need to take a train to Gorakhpur (around three hours from the border in Sunauli), a jeep or bus to the border, and another jeep or bus to Kathmandu from there.
The best train from Varanasi is the Chaurichaura Express (#15003). It's an overnight train that departs Varanasi at 12.35 a.m. and will have you in Gorakhpur at 6.50 a.m., just in time to take a jeep or bus to the border, cross, and take a morning jeep or bus to Kathmandu. The Gorakhpur Express (#15017) is another option for getting from Varanasi to Gorakhpur. However, this train runs during the day (departs at 1 p.m. and arrives at 7.10 p.m.), necessitating a stay in horrible Gorakhpur the night. Expect to pay 155 rupees in Sleeper Class up to 510 rupees in 2AC for the train journey (more about classes of accommodations on Indian Railways trains).
Varanasi to Kathmandu Buses
The cheapest and longest (and also the most uncomfortable) way to get from Varanasi to Kathmandu is to take the bus. It's an unenviable 20 hour journey, consisting of 10 hours to get to the border in Sunauli, and then another 10 hours to Kathmandu from there. There are two options for taking the bus: book a through service all the way from Varanasi to Kathmandu, or book one leg to Sunauli and the second leg from Sunauli to Nepal when you get there.
If you book a through bus, your journey will usually start early in the morning and be broken up by an overnight stay in Sunauli (not an appealing prospect, it's not a good place to be) and you won't get to choose your bus from Sunauli to Kathmandu (you have to change buses there). You'll have more flexibility and save money by doing the two legs separately. Buses leave from Varanasi to Sunauli throughtout the day from around 5 a.m to 8 p.m. At Sunauli there are both morning and overnight buses to Kathamandu. It's best to take a morning one because it's faster and you get to see the incredible scenery on the way. Cost: under 1,000 rupees for the complete journey.