You can board a bus in Kathmandu that will take you to Nepalgunj. If you are allergic to bus rides, it’s possible to fly to Nepalgunj and cut the bus travel down to about 4 hours on the way over and two hours on the way back. From Nepalgunj, you can go to Surkhet on a bus or you could board an airplane. From Surkhet you could go on a lovely two day trek to Sauli, from where it is a two hour trek to the Karnali River.
Please click here to know more about rafting in Karnali River.