Simandl New Method for Double Bass
All bass players of any age and experience should own this book (it is the classic reference book, along with the advanced follow up book II), and then also own the more modern studies of open-hand fingerings, melodic or solo fingerings, speed fingerings (American School of Double Bass - Mark Morton, ), and/or something from the "New Dutch Method," and tedious, but well worth carefully examining,"The School of Agility" by New York Philharmonic principal Eugene Levinson (it is basically three octave scales and arpeggios with bowing variations, but everyone should play whatever bits and pieces they can manage -- the excitement comes when you find you magically can play things you never imagined you could without thinking too much).