Actually, in my mind, book season is 365 days each year.
Writers and readers do have seasonal conferences, luncheons, and events. And the season is starting.
Are you a writer? Have you scoped out the conferences or workshops in your area? Don’t know where to start? Check in your local library for any sort of writing magazine — they often have advertisements and listings of popular, reoccuring events. Another good source is the web page of writers groups.
Are you a reader? Spring, summer, and fall are popular times for reader events. Meet new authors. Browse book tables. Get filled with the “new book” smell. Find other readers — you may find new friends among them.