Ummm...well I don't know how you would get a spell book.
It might be an option I'm unaware of, but an Arcane Sorcerer get's the arcane bond as per the wizard class feature. However:
Arcane Bond (Ex or Sp): At 1st level, wizards form a powerful bond with an object or a creature. This bond can take one of two forms: a familiar or a bonded object. A familiar is a magical pet that enhances the wizard's skills and senses and can aid him in magic, while a bonded object is an item a wizard can use to cast additional spells or to serve as a magical item. Once a wizard makes this choice, it is permanent and cannot be changed. Rules for bonded items are given below, while rules for familiars are at the end of this section.
Wizards who select a bonded object begin play with one at no cost. Objects that are the subject of an arcane bond must fall into one of the following categories: amulet, ring, staff, wand, or weapon. These objects are always masterwork quality. Weapons acquired at 1st level are not made of any special material. If the object is an amulet or ring, it must be worn to have effect, while staves, wands, and weapons must be held in one hand. If a wizard attempts to cast a spell without his bonded object worn or in hand, he must make a concentration check or lose the spell. The DC for this check is equal to 20 + the spell's level. If the object is a ring or amulet, it occupies the ring or neck slot accordingly.
A bonded object can be used once per day to cast any one spell that the wizard has in his spellbook and is capable of casting, even if the spell is not prepared. This spell is treated like any other spell cast by the wizard, including casting time, duration, and other effects dependent on the wizard's level. This spell cannot be modified by metamagic feats or other abilities. The bonded object cannot be used to cast spells from the wizard's opposition schools (see arcane school).
A wizard can add additional magic abilities to his bonded object as if he has the required item creation feats and if he meets the level prerequisites of the feat. For example, a wizard with a bonded dagger must be at least 5th level to add magic abilities to the dagger (see the Craft Magic Arms and Armor feat in Feats). If the bonded object is a wand, it loses its wand abilities when its last charge is consumed, but it is not destroyed and it retains all of its bonded object properties and can be used to craft a new wand. The magic properties of a bonded object, including any magic abilities added to the object, only function for the wizard who owns it. If a bonded object's owner dies, or the item is replaced, the object reverts to being an ordinary masterwork item of the appropriate type.
If a bonded object is damaged, it is restored to full hit points the next time the wizard prepares his spells. If the object of an arcane bond is lost or destroyed, it can be replaced after 1 week in a special ritual that costs 200 gp per wizard level plus the cost of the masterwork item. This ritual takes 8 hours to complete. Items replaced in this way do not possess any of the additional enchantments of the previous bonded item. A wizard can designate an existing magic item as his bonded item. This functions in the same way as replacing a lost or destroyed item except that the new magic item retains its abilities while gaining the benefits and drawbacks of becoming a bonded item.
So, a bonded spell book isn't a option as far as I'm aware.
Besides which, the arcane bloodline states this:
Arcane Bond (Su): At 1st level, you gain an arcane bond, as a wizard equal to your sorcerer level. Your sorcerer levels stack with any wizard levels you possess when determining the powers of your familiar or bonded object. This ability does not allow you to have both a familiar and a bonded item. Once per day, your bond item allows you to cast any one of our spells known (unlike a wizard's bonded item, which allows him to cast any one spell in his spellbook).
So, no. You can only cast a spell you know. Basically you get an extra spell slot for free of any spell level you are capable of casting.
Unless there are some special options I am unaware of, what you're suggesting doesn't work.
And no, having a spell book doesn't give you more spell known unless handing a spell book to a fighter gives him spells known. It is not a class feature for a sorcerer, nor is it for a fighter. A spell book is a book of stuff you can't use either way. Except to sell it.
Bonded book is not currently an option. There was a 3PP feat that facilitated it. I'll link it if I can find it.
I rather like the idea actually. However, i'm not sure i'd want the source of my power present and visible in a fight. Cool visual effect though.
Note that a sorcerer CAN USE a spell book.
There is a feat, came out of PFS, that allows a sorcerer to prepare a spell from a spell book.
There is also a Ring that allows a sorcerer to peruse a spellbook or scroll and instantly 'hold' it as a Spell Known.
Both are extremely useful for a sorcerer.
==Aelryinth
Well that deters that thought. I always imagined bonded items were open to the player and GM. I didn't know there were categories that it had to fall under.
Also there's a defined difference between a Sorcerer and a Fighter, in that Sorcerers can read spells even if through magical means. Fighters wouldn't normally be able to do that unless the fighter was seeking out magical pursuits, such as multi-classing into magus.
Well then, lets take a rogue who uses the talent to get read magic as a cantrip. He can read the spell, but still doesn't have a spell list. You're ability is no greater than the rogues, with regard to usimg the spellbook. You can read the spells, but that doesn't mean you know them.
Anyways, as pointed out bonded spellbooks aren't an option.
what feat Aelryinth?
The feat is probably Versatile Spontaneity
Ring: There are Rings of spell knowledge.
In a similar vein, there are Mnemonic Vestments
There is also the fact that a character with arcane bond has to have the item in use for the spell caster to even cast spells. This would mean that to cast any spell you would have to have the book in hand or make a concentration check to avoid losing the spell slot. Even if this worked it would be a terrible idea.