The worry and fear about blushing sets us up to blush more often. It is the fear of blushing, and how we think others view it, that "convinces" us that blushing is a dreadful thing. However, the act of blushing itself is not an "automatic negative thought" or ANT.
If you blush, then that is just an unfortunate fact of life right now.
By definition, an automatic negative thought (ANT) is irrational, and it is always wrong. You are right: If you feel that everyone notices you blush, is judgmental about it, and thinks less of you because of it, these are automatic negative thoughts.
People who are not blushers do not feel that blushing is terrible, awful, or embarrassing. Most often, they don't even notice it. If they do notice it, it is because you pay attention to it, point it out, make a comment about it, or look embarrassed, humiliated, and defeated by it
Conversely, if you continue right on with what you are doing or saying when you blush and, if you put no effort into concentrating on the symptoms, others will not usually even notice it. Even if they do, you will have learned not to care.
First, cognitive therapy for social anxiety directly address all the "germs", catalysts, or triggers involved in the cycle of blushing maintenance. Since blushing is maintained by our anxiety, in cognitive therapy we learn to think, believe, and feel differently than we have in the past about our anxiety.
Sometimes people want "blushing only" therapy. We learned very quickly that this does not work, because the root cause of blushing is social anxiety. For blushing to be eradicated, then social anxiety must be eradicated, too. Cognitive therapy to overcome social anxiety and its symptoms, whether it be blushing, excessive sweating, hands that shake, or neck twitching, is always necessary.
So, adopting a "so what, who cares" attitude and taking the pressure off yourself is the best solution. This is very hard to do on your own, and happens much more frequently in the context of an active, structured social anxiety therapy group
Overcoming social anxiety (and blushing) is a paradox. It is only when we learn to stop fighting, struggling and trying to force the anxiety away that we can start to recover from social anxiety. This requires persistence, patience and a willingness to be kind to yourself.