Is there any yellowing associated with the bumps? It sounds a little bit like cedar apple rust, a fungal disease. Some varieties of apple are susceptible to cedar-apple rust and others are not, so it wouldn't be unusual for just one tree out of 5 to show symptoms. One way to control cedar-apple rust is to remove all junipers within a half mile. Because that is seldom possible to do, you may have to spray the tree with a fungicide to prevent the disease from developing. Alternatively, you could replace the susceptible tree with a resistant variety.