Is it better to take a bus or a flight?

If you are already at the border, the bus is the only practical option. Flying would require traveling back to a city like Gorakhpur in India to catch a flight to Kathmandu, which defeats the purpose of the land crossing.

Are the night buses safe?

Generally, yes. They are the standard way locals and backpackers travel. Keep your valuables in a small bag that stays on your lap rather than in the luggage hold under the bus.

Getting from the Nepal-India Border to Kathmandu

Most travelers cross at the Sunauli-Belahiya border and take a direct night bus to Kathmandu. The journey takes 10 to 12 hours depending on road conditions, and you should book your ticket at the bus station or through a local agent immediately upon crossing.

Cross the border at Sunauli. Walk across the border from India (Nautanwa) into Nepal (Sunauli). Get your passport stamped at the Nepalese immigration office on the left side of the road. Ensure you have two passport-sized photos for your visa if you are getting it on arrival.
Exchange money. Exchange a small amount of Indian Rupees to Nepalese Rupees (NPR) at the border money changers to pay for your rickshaw or initial snacks. The rate is pegged at 1.6 NPR to 1 INR.
Locate the bus park. Take a cycle rickshaw (100–150 NPR) from the border to the Sunauli bus park. Do not let the driver convince you that the buses are sold out; they receive commissions to take you to specific private ticket offices.
Purchase your ticket. Go to the official bus counter. Ask for a 'deluxe' or 'air-suspension' bus to Kathmandu. A night bus leaving around 5:00 PM is best so you arrive in Kathmandu the following morning.

Is it better to take a bus or a flight?: If you are already at the border, the bus is the only practical option. Flying would require traveling back to a city like Gorakhpur in India to catch a flight to Kathmandu, which defeats the purpose of the land crossing.
Are the night buses safe?: Generally, yes. They are the standard way locals and backpackers travel. Keep your valuables in a small bag that stays on your lap rather than in the luggage hold under the bus.