You may arrive in Loei from
1) BKK (Northern Bus Terminal) about 10 hours (exhausting)
2) Phitsanaluke about 4 hours
3) Udon Thani: about 4 hours (the road is unimpressive but you may have a stop in Erawan Cave)
4) Khon Khaen: about 4 hours (the first part is busy and boring, but the second one is fine, when you travel cross mountains).
The best choice from BKK, if you are not in a hurry, is take a bus to Phitsanaluke, stop, and the day after take the bus to Loei (this second part is very beautiful, so don't sleep during the trip).
To Chiang Khan the bus started at western end of town, but the problem is on return because they unrealible. Better choice is hire a songthaew (bargain hard)
I went to Loei via Lom Sak. I started from Phitsanaluke going to Lom Sak; before Lom Sak there are a lot of accomodations if you need a stop. Then, following 203 you arrive in Loei. Be careful you have to drive to 203, before entering in Lom Sak, or you are lost. I spent about 1 hour lost in the town.
There are a few ways to get to Loei-all by bus. We flew into Udon Thani by Bangkok. From there we went to Laos( Vientiane) thru Nong Khai (Thai border town). From Nong Khai you can take the 507 bus, which is a scenic bus that hugs the Mekong River. Lonely Planet even recommends doing the ride-since it's quite beautiful and extremely rural. Not many people speak english and they really want to communicate with you. So bring a phrase book. This ride took around 5-7 hours to Loei, our bus broke down for a hour or so.
For a faster ride, you can take a bus from Udon thani to loei. I forget the bus number. But the ride was around 3 hours. Much shorter.
From Chiang Khan to Loei,there're 2 kinds of bus run between this places. One 's air con bus ,which you can take any one which pass the city center and drop at the Loei bus terminal ,take about half and hour and around 30 B per trip (but the departure time may need to check before).
Another kind 's Songteaw (mini bus) run between 5.00-20.00 every 20 minutes ,take about 1 hour per trip ,cause it always stop and wait for more clients. Price is 20 B. You can it at the bus terminal.
From Bangkok, Northern Bus Terminal (Morchit),there're some buses run directly to Chiang Khan. For V.I.P (24 seats) 540 B for 10 hours. Depart 22.00
1st class 347 B for 10 hours .Depart 7.30 and 19.30