The difficulty or ease of getting a travel visa for a Thai lady to enter your country varies greatly from country to country. I have not yet had the time to address the issue in regard to any countries other than my own, the U.S., as covered below, and I would like to hereby solicit inputs from others who are citizens of other countries so that I may post them here for the benefit of your compatriots.
If you're legally married in Thailand, i.e., a signed, registered marriage, which is a whole other process that will also involve your embassy/consulate in documentation, then getting a travel visa is usually not difficult. However, just going through the Buddhist ceremony isn't the same thing. (You can take lots of photos, which can help your chances in getting another kind of travel visa, but it's not the same as a registered marriage.)
The process is for your Thai girlfriend to get a Thai passport, then for you and her to apply at your embassy or consulate in Bangkok for a travel visa to your country. The first thing you should do is inquire with your consulate for a list of required documentation. You should also seek out others from your country who have done this before, to get a feel for how your embassy/consulate handles matters, and for tips.
Your embassy/consulate can reject a visa application without stating any reason. Just because they have given you a list of documentation to bring together doesn't mean that if you follow all the procedural steps then you will get a visa.
Further, you want to give it your best shot the first time, and not submit an application to see if it's rejected before you go to great efforts. Your girlfriend does not want to get a rejection noted in her passport. Notably, most embassies/consulates don't put any ugly "rejection" stamp in the passport, but do stamp that a visa was applied for on a particular date. If there's no corresponding visa stamp (essentially an approval), then a subsequent officer will probably take note and read between the lines -- a rejection. This is standard procedure. In fact, they'll often put the "visa applied for" stamp into the passport as they're handing it back to you after telling you that you've been rejected.
The reason for these problems is obvious. People from less developed countries want to immigrate to rich countries so that they can work there and make more money. If international travel were free, then the rich countries would soon be overrun by people from less developed countries. The domestic governments would be overwhelmed in dealing with people working and staying there illegally. To some extent, they already are. In fact, countless people from less developed countries get entangled in mafia circles whereby they work in overseas sweatshops or brothels, or meet a worse fate.
Some kinds of Thais have little or no problem getting visas. One example is wealthy businesspeople who are obviously going for business or a short vacation. Another example is students who wish to study at a foreign university and who have good grades, speak the foreign language very well, and are from well to do families. Highly educated people who have a high tech skill in short supply relative to demand in another country can often get a visa and work permit. (The latter is an unfortunate phenomenon called "brain drain", where the most valuable people leave their own country.)
Besides that, the things your embassy/consulate will be looking for are reasons for them to return to Thailand, e.g., land ownership and major assets, money in the bank over a long time (looking thru past bank books over time), and/or a good job in Thailand. If your girlfriend has a 6th grade Thai government school education, no business of her own, and no assets besides a little farmland in the middle of nowhere with a buffalo, then her chances are often slim.
Bar girls are routinely rejected. They usually can't even read English (or any other western romanized language), are high risk to not return before their visa expires, and are seen as likely to be prostitutes and/or get into problems in the other country. The embassies/consulates are also used to dealing with lonely foreigners who have come to Thailand on a short visit and with awesome naivete think they have met the girl of their dreams in a bar, who they think will be grateful and loving ... blah, blah, blah.
