For one, it is crucial that the bribed individual is regarded as a public official. A public official could be a federal employee, such as someone who works at the NSA, or an elected official, such as a Senator.
Another significant element is that something of value must be offered in exchange for an official act influenced by the bribe. However, the public official must possess adequate authority to commit the offense. For example, if someone attempted to bribe a city mayor to start a war with another country, that would be insufficient to support a federal bribery charge since a city mayor does not have the power to start a war.
The briber must also establish that they desire a specific, beneficial result from the bribery. The prosecution has the burden of proving beyond a reasonable doubt that there is a causal connection between the value offered and received and the official act carried out.