The CIA absolutely bribes local officials. The issue is you need to bribe the right people:
1. People who will change their opinion, reliably, when bribed.
2. People who won't backstab you (aka: take the money, and attack you anyway).
Figuring this out is an intelligence problem. To get good intelligence, you need boots on the ground. To have boots on the ground, you need to protect them. Etc. etc.
With regards to Afghanistan culture: they have a different way of thinking than us Americans. Sure, some can be bribed with money, but a history of being a warzone for... I think 200 years at least... has made their culture strange and alien to us.
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IIRC, Afghanistan culture is about accepting and protecting of strangers, even when they are under attack. But as soon as the stranger leaves, you're allowed to shoot them or otherwise kill them again. So this makes #2 more difficult, you need to understand the local's religion, their culture, their legends and their stories. (I'm probably butchering the concept, but I read about the details a long time ago...)
In the case of Afghanistan, if US Troops could take advantage of the "accepting of strangers" culture, then US Troops will be protected by the locals. Diplomacy leads to better war-fighters and safer people. Play your cards right, and you don't even need to bribe people. You'll be a good-guy in their culture and they'll protect you.