Different types of bonuses stack together, but multiple bonuses of the same type usually do not. If you have two of the same type of bonus, only the better one applies. Unnamed bonuses alway stack. The named bonus types are as follows.
Armour: An armour bonus represents something that passively stops an attack hitting a vulnerable area.
Circumstance: A circumstance bonus represents situational factors. Circumstance bonuses stack if they are caused by different circumstances.
Competence: A competence bonus represents getting better at doing whatever it is that the bonus applies to.
Dodge: A dodge bonus represents getting out of the way more quickly. Dodge bonuses always stack.
Enhancement: An enhancement bonus represents an improvement to an existing ability, skill, or property.
Luck: A luck bonus represents good fortune, such as close misses, fortunate hits, and serendipity.
Shield: A shield bonus represents something that actively stops an attack hitting a vulnerable area.
Size: A size bonus represents the effect of getting bigger.
Natural Armour: A natural armour bonus represents naturally tough skin that passively stops an attack hitting a vulnerable area.
Resistance: A resistance bonus represents increased resilience against magic and injury.