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Looked at the Duelist weapon enhancement and noticed it provides a +4 enhancement bonus to init.
Naturally with a +11 (trying for 18+) Init. I thought this would be a prime get, but then remembered my belt of Dex +2 adds an enhancement bonus to me Dex, which in turn adds to my init.
So, does the enhancement bonus to dex translate into an enhancement bonus to init. as well?
No it doesn't. It's a bonus to your Dex which has the side effect of raising your Initiative -- but you don't have an enhancement bonus to Initiative yet so you are good to go with getting one.
Derp misread the response. So yes those two bonuses stack just fine OP, they are in fact different bonuses.
To break it down a little bit... Enhancement bonuses apply to very specific things. In determining whether an enhancement bonus stacks with another enhancement bonus, you must first determine what each enhancement bonus is actually enhancing.
An enhancement bonus to Dexterity would increase your Dexterity Score, which in turn means you have a higher Dexterity modifier. An enhancement bonus to Dexterity does not, in that way, directly increase your Dexterity modifier (though it is a close thing.) (In other words - a +6 enhancement bonus to Dexterity doesn't increase your Dex modifier by +6.)
An enhancement bonus to Initiative would increase your Initiative score. So you can see your Initiative score as:
Init = Dex Modifier + Feat Bonuses + Trait Bonuses + Enhancement + Miscellaneous
Because the enhancement bonus to Dexterity only indirectly raises your Dex modifier, it stacks with your initiative enhancement. The same way that an enhancement bonus to dexterity stacks with your enhancement bonus to your Armor Class - they affect completely different numbers, and thus stack.
(Which is also why an enhancement bonus to Natural Armor stacks with other enhancement bonuses to AC. The enhancement bonus to Natural Armor is specifically increasing the natural armor bonus, which in turn is used in calculating Armor Class.)