To answer the question, there is a grey area between bribery and lobbying. As long as the lobbyist does not violate the law by giving more money than is allowed to a member of congress, and by not explicitly saying that the money is for a vote (one way or another on a particular piece of legislation), it is not considered bribery.
Lobbyists will often take legislators on really fancy vacations that are called 'fact finding missions', where everyone stays at a really nice golf resort or something and the lobbyist hasn't actually given the legislator any money, so no laws have been broken. At the end of the day, the legislator can decide to vote however he/she wants, so again, they don't consider it bribery.
So, what is bribery of a legislator in the U.S.? You'd probably need someone on tape saying, "I'll vote yes if you give me 200 grand in this swiss bank account". (Or, more simply, see: Rod Blagojevich.)
Also, surveys have shown that all those donors are giving because they already agree with the senators' views, not because they think they can influence them.