For instance, could a fund be created that would only be rewarded to a particular re-election campaign if the representative votes a particular way on a bill?
Individuals can choose to act that way in deciding where their money goes, but it is illegal to set up any kind of formal arrangement that explicitly gives money for particular votes or actions (the now very famous "quid pro quo"). Setting up a fund and announcing that it will conditionally award money for certain actions would certainly and pretty clearly run afoul of existing US laws.
Not that there isn't a ton of gray area if someone wanted to be more subtle about it. There's a lot of unresolved conflict between the idea of money being used to improperly influence officials and campaign money being the equivalent of "speech."
Federal law makes it a crime to corruptly solicit or accept money with the intent of being rewarded or influenced in official actions, and prosecutors have said campaign contributions can be part of such a scheme.
The Supreme Court's guidance on the issue is thin. In 1991, it ruled that a campaign contribution could be a bribe if the prosecutors proved a quid pro quo - that the contribution was "made in return for an explicit promise or undertaking by the official to perform or not perform an official act."
In a subsequent case, Justice Anthony Kennedy said the quid pro quo not be expressly stated. But the lower courts have differed, since then, on exactly what standards apply.
There are ways that this happens legally all the time.
Multiple issue-oriented organizations (NRA, Planned Parenthood, just to name two) may announce that they will be grading Congresspeople based on particular bills/votes, and will not consider contributions unless the Congressperson reaches a "passing grade" on their particular issue.
The Congressperson is free to vote their conscience, and suffer the consequences (or reap the rewards) when campaign season comes. An individual can do the same (and many people actually do: refusing to donate because of a particular vote, or increasing a donation based on another vote)
An individual may pledge money towards an opponent if an Elected Official votes "incorrectly", with the tacit understanding that if the E.O. votes "correctly", an opponent will not get extra funding. The Elected Official is not bribed, but will still risk a better funded opponent during the next campaign based on their vote.