You get one attack roll for each natural attack you possess, and you do not get any extra natural attack for high BAB (you still gain extra weapon attacks though)
This is not clearly stated in the rules, but before justifying why the rules intention is that one, let me introduce where the confusion comes and why it is justified.
First of all, the rule which states you get extra attacks as your Base Bonus Attack (BAB) rises. Under common terms definition:
Base Attack Bonus (BAB): Each creature has a base attack bonus and it represents its skill in combat. As a character gains levels or Hit Dice, his base attack bonus improves. When a creature's base attack bonus reaches +6, +11, or +16, he receives an additional attack in combat when he takes a full-attack action (which is one type of full-round action—see Combat).
So by the BAB rule you get additional attacks when you reach certain BAB levels.
Let's check what the natural attacks rules say:
Natural Attacks: Most creatures possess one or more natural attacks (attacks made without a weapon). These attacks fall into one of two categories, primary and secondary attacks. Primary attacks are made using the creature's full base attack bonus and add the creature's full Strength bonus on damage rolls. Secondary attacks are made using the creature's base attack bonus –5 and add only 1/2 the creature's Strength bonus on damage rolls. [...]
Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (although often a creature must forgo one natural attack for each weapon clutched in that limb, be it a claw, tentacle, or slam). Such creatures attack with their weapons normally but treat all of their natural attacks as secondary attacks during that attack, regardless of the attack's original type.
So nowhere says natural attacks do not get extra attacks for high BAB, but it neither says they do, and it makes a clear difference between natural attacks and attacks made with weapons. So the intention seems clear that natural and weapon attacks are different things and work differently.
Now, the WHY of the answer. We can infer how this works from examples. In this case take a look to the Bear in Paizo Bestiary. At one side we have the Grizzly Bear (BAB +3) at the other the Dire Bear (BAB +7):
Melee 2 claws +7 (1d6+5 plus grab), bite +7 (1d6+5)
Base Atk +3; CMB +9 (+13 grapple); CMD 20 (24 vs. trip)
Melee 2 claws +13 (1d6+7 plus grab), bite +13 (1d8+7)
Base Atk +7; CMB +15 (+19 grapple); CMD 26 (30 vs. trip)
As you can see the Dire Bear has +7 BAB, which corresponds to an attack iteration of +7/+2, but if you look at the Dire Bear attacks, he has exactly the same number and type of attacks than Grizzly bears. Thus, it seems that Pathfinder developers intention is high BAB does not give you access to additional natural attacks, and that is something reserved to weapon attacks, unnarmed strikes and combat maneveurs.
Remember you need to take a full-attack action in order to perform all your natural attacks, and you still benefit from additional attacks if you are holding at least one weapon.
Addendum about natural attack bonuses
When performing multiple natural attacks, you have also to take into account the difference between primary and secondary attacks. So let's see when a natural attack is considered primary or secundary based on the universal monster rules:
Primary: You attack with full BAB and full Strength damage bonus. Are considered primary:
- Typical primary natural attacks: Bite, Claw, Gore, Slam, Sting, Talons
- Whatever attack if it is the only type of natural attack the creature has (be it single attack as a Tile Slap, or multiple as 2 Pincers)
Secondary: You attack with BAB -5 and half Strengh damage bonus. The multiattack feat reduces this penalty from -5 to -2. Are considered secondary:
- Typical secondary natural attacks: Hoof, Tentacle, Wing, Pincers, Tail Slap, Others...
- Whatever attack if it is used in combination with weapon attacks (including unarmed strikes).