Your main concern, I think, should be that your doctor will immediately refer you to a surgeon, and the first impulse of the surgeon will be to repair it with whatever method in which they have received training. Once they are in there they might see other defects which will give reason to do more repair. The most common repair method today is mesh. It’s very possible that you end up with coverage of most of your lower abdomen with mesh, if you mention any symptoms of inguinal hernia, like twinges in the groins. I saw a surgeon for a very simple direct hernia, one side, and after surgery I had bilateral implantation of as much mesh as he could fit in to the space.
That would be extreme, I think, for an umbilical hernia, but the training today is that mesh is harmless if implanted correctly, therefore more is better, for prophylactic purposes. The path from consultation to surgery can be very fast and smooth, and comfortable. Hernia repair is a mainstay of many surgical practices due to the high volume. So take your time in making a decision. You will probably hear about how it could get bigger, and strangulation of bowel could occur, and how the procedure is an outpatient procedure with no hospital stay necessary. But the long-term effects should be your main concern.
I don’t have any advice on reducing the bulge. My direct hernia bulge was not reducible either once a certain amount of material got out. I think that if the defect is small the material that gets out can’t be pushed back once the peritoneum gets stretched out of shape.
Dr. Kang has posted on the site about non-mesh umbilical hernia repair. You might read some of his posts. Good luck.