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.