You are right, there is no one textbook for serials, but you could start
with these:

Marcia Tuttle's Introduction to Serials Management (a little old now, but
covers the most of any other book out there)

Marcia Tuttle and Jean Cook's series: Advances in Serials Management
I believe 3 volumes have appeared to date.

NASIG proceedings (published by Haworth separately or as part of the
  Serials Librarian)

Serials Librarian (some special theme issues)
Serials Review

There are others with differing emphasis--serials cataloging, acquisitions,
journal publishing, but I would highly recommend all of the above as the
best starting point.

Susan Davis        (maybe also check the Year's Work in Serials in LRTS for
Head, Periodicals      the past several years to put together a reading list!)
State University of NY at Buffalo