Finding truly vegetarian Thai food, that would even be acceptable to people that live a vegan lifestyle is hard to do, regardless of whether you are looking inside or outside of the borders of Thailand.
It's a common misconception that there are many regular Thai vegetable dishes that are suitable for vegetarians.
Even thought most Thais, particularly those of Chinese descent, are known to spend several weeks a year eating strictly "Jay"or "Jeh" food (a term which is commonly translated to vegan in english), it is rather difficult to find thai vegetarian food that would also be suitable for the true vegetarian or vegan.
Many of the Thai vegetarian dishes are prepared by using ingredients like oyster sauce and fish sauce, while even the seed based sesame sauce can contain some animal extracts.
The best places to find a true vegetarian meal in Bangkok, or anywhere else in Thailand for that matter, would probably be at the local Indian restaurants. Several can be found in the Indian districts, of which most seem to be located on the western side of the Bangkok.
Alternatively, one can always have an proper vegetarian lunch and / or vegan dinner at one of the many international 4 or 5 star hotels that the city holds. These large hotels' kitchens cater to vegetarians from many countries around the world and thus have to ensure that all ingredients are 100% free of animal products or derivatives.