I would say "Will you tell Jenny that I said hello the next time you see her?"
Your second sentence would sound much more natural as: "I'll call you the next time I'm in town." I don't think your version sounds correct with or without the "the". You could also say "I'll call you if I'm in town again."
"I'll bring a book to you next time" is fine.
*** Not a teacher ***
Student or Learner