Can I study on GI-Bill in Thailand?
Sure you can. Welcome!
If you are eligible for one GI Bill, you get a benefit of 36 months. This should be enough at some Thai universities to graduate from a Bachelor degree program. Bachelor programs are always 4-year programs, but some universities offer additional courses during the Summer Session that help you cut down the duration of your studies by a full year.
If you are eligible for two GI Bills, you can use both your Montgomery GI Bill (MGIB) and your Post 9/11 GI Bill to study at a university in Thailand with a combined benefit of 48 months. If you are eligible for both and you are thinking about going beyond a four-year degree, then you might want to look at using your Montgomery GI Bill first and then switching to the Post 9/11 GI Bill (source). The other way around is not possible, so you would lose 12 months' benefits.
If you are not sure about your eligibility or benefits, the VA Department make a grade Benefit Comparison Chart. That page also offers access to some case studies for both Active Duty and Reserves.
Although there's a payment difference between both GI Bills, it should be enough to study any single degree undergraduate program and have a comfortable life as well, due to the still very low cost of living in Thailand, if compared to western countries and the U.S.
To enjoy your benefits, the program of education you want to study must be approved. Following Thai universities have the necessary approval. The links point to the original list from where you can access institution profile, maximum benefits, and programs approved. Please note: It is not sufficient that the university has the approval - the program of education you want to study must be approved!
Dhurakij Pundit University
King Mongkut's Institute of Technology, Ladkrabang
Mae Fah Luang University
Mahidol University International College
Prince of Songkla University
Rangsit University (International College)
Sripatum University Chonburi Campus
If the program of your choice is not approved yet, here is the process: 15 questions must be answered (in case of medical schools, it's a bit more). They cover the minimum information to be included in requests for approval of foreign training programs (follow the link to the official source). With a little help from some halfway English speaking staff you will get that done. The Veterans Affairs Department is quite flexible - it will not need years to complete the process.