From Kathmandu, you can take a tourist bus from Gongabu Bus Park (http://goo.gl/RyvWYL) going in the direction of Butwal and get out at Danda. The ticket will cost around $10, and the journey takes around 5 to 6 hours.
From Pokhara, you can take a local bus from the Tourist Bus Park (http://goo.gl/FuF7pL) going in the direction of Butwal and get out at Danda. The ticket will cost around $10, and the journey takes around 4 to 5 hours.
Once you reach Danda, you will need to take a tuk-tuk to Barauli. The trip takes about 30 minutes and costs 70 rupees per person.
Alternatively, we can arrange private transport for you:
Kathmandu-Barauli Community Homestay is located inside Chitwan. You can access this area on your own by public transport. From Kathmandu, you can get a tourist standard bus from Gongabu Bus Park (http://goo.gl/RyvWYL), also known as New Bus Park. The bus ticket will cost around $10. It will take around 5 to 6 hours, depending on the traffic. Make sure you take the bus going to Bhairahawa, Sunauli, or Butwal and get down to Danda.
From Pokhara - Similarly, if you are going to Barauli from Pokhara, you can get a bus from Pokhara Tourist Bus Park. Similarly get down at Danda while going to Barauli from Pokhara as well. The ticket will cost approximately $10, and the journey will take 7 hours, depending on the traffic.
From Palpa - As for the location from Pokhara, you have to catch a bus that goes to Butwal from Pokhara Tourist Bus Park. You have to get down at Danda Bazaar. From Danda Bazaar, you have to take a tuk-tuk vehicle that goes to Barauli. The journey would take 6-7 hours, approx.