There seems to be a general misunderstanding of how natural attacks work. Either that, or how you describe things is really weird.
Natural weapons mostly work just like regular, i.e. manufactured weapon. The existence of a weapon in itself doesn't allow you to make attacks, you need to use an existing rule for that. All characters have the options to make attacks via the standard Attack Action, the Charge action, Attacks of Opportunity (all of these are a single attack), or the full-attack action, with sometimes additional options from feats (like Cleave) or class features (like Flurry of Blows). The main difference natural weapons have that when you use the full-attack action, instead of gaining iterative attacks (the bonus attacks at BAB+6 etc.) you instead can make one attack with each natural weapon you have. Stuff like Haste is seperate added on top either way and is a single extra attack.
Apart from extremely rare exceptions, the standard attack action is always a single attack. Apart from some specific feats, in order to make more than one attack per round, a creature must use the full-attack action.
The "Melee" line in a creature's stat block always describes a possible full attack. When natural weapons are involved, it also serves the purpose of listing those. For a Flesh Golem, the melee section says "2 slams +13 (2d8+5)". If the golem uses the full-attack action, it can make two attacks, one with each of its slam natural weapons (of which it has two). Haste would allow it to chose one of these slams and make another attack with it as part of the same full-attack action. If the golem uses the standard attack action (or makes a charge attack, or an AoO), it only can only make an attack with one slam.
A Bone Golem's melee line says "bite +14 (1d8+4), 2 slams +14 (2d6+4)", that means it has three natural weapons (bite, slam, slam). As a full-attack action, it can make one attack each with all three. When hastened, it can chose one of these three natural weapons an make a bonus attack with it. As the attack action, charge, or AoO, it has to chose one of the three to make the single attack with it.
The +13 or +14 are not the "BAB" (that's listed further down in the stat block), but rather the attack roll bonus, which includes BAB, strength, and possibly other bonuses or penalties. Haste would add +1 to that, for instance. A hastened Clay Golem thus has, in effect, a melee line of "3 slams +20 (2d10+7 plus cursed wound)".
Just in case, the iterative attacks, i.e. bonus attack gained from having high BAB (+6, +11, +16), are only for manufactured weapons and unarmed strikes, that rule does not apply to natural weapons. That's compensated by being able to use multiple weapons in the same full-attack action, and gainign an attack each, without penalties.
Edit @Matthew: Thanks, fixed.
Apart from some specific feats, in order to make one attack per round, a creature must use the full-attack action.
I think you mean "in order to make more than one attack per round"?