The following book has a nice and long chapter of BV functions in one variable:
G. Leoni, A First Course in Sobolev Spaces Graduate Studies in Mathematics Volume: 181.
Also an excellent book covering a great deal of the material is:
I. P. Natanson, Theory of functions of a real variable. Translated by Leo F. Boron with the collaboration of Edwin Hewitt. Frederick Ungar Publishing Co., New York, 1955.