No. It is not difficult to be vegetarian in Myanmar.
It is difficult speaking to the locals if you do not understand the local language, but there are plenty of vegetarian options available.
Unlike in Japan and China, the concept if you can communicate it to your host, is typically understood. You may need to specify that you do not wish to have fish in your meal, but due to the ethnic diversity, they will understand that there are people who choose not to eat all forms of meat. Try saying that in Japan, and they will just think you eat fish. Or chicken. Or some other strange form of animal anatomy which you did not even know existed.
In some of the more touristy places, there are western restaurants where it is possible to find western and vegetarian food, like pizza and pasta.
In Bagan, there are restaurants titled “vegetarian restaurants”. However, I also saw one serving meat, so do not lower your guard too much.
Chef’s typically are very accommodating, so if you ask for a meal without the meat it should not be too much of a problem.
The food often gets described as a mix between Thai, Chinese and Indian – which is a bit simplistic, but not too far from the truth either. One thing is for sure is that the food is very, very greasy.
All in all, you should not have too much trouble as long as you are a little bit discerning. And patient!