Probably not illegal and definitely not a "bribe" in the sense of criminal bribery (which must involve some official action or refraining from official action).
Access can be legally conditioned on payment of money in many cases, even though it can't be for the politician's personal (as opposed to his or her campaign fund's) benefit. (I don't rule out the possibility that there are some exceptions that are not legal but none come to mind at the moment.)
Arguably the friend arranging the meeting is an unregistered lobbyist and so it might be a technical violation of that law by the unregistered lobbyist, and that technicality, if present, might render the contract unenforceable by either party in a court of law. But assuming that this takes place in a jurisdiction that doesn't require lobbyists to register it probably isn't illegal, and assuming that the payment is made and the access is given without complaint, the legality of the contract is irrelevant.
As a practical matter, this kind of access for money is usually done as a campaign contribution incentive by the candidate or an affiliated campaign fundraising entity. Lobbyists who try to arrange contacts with politicians usually work on flat monthly retainers in exchange for their best efforts, rather than on a fee for service basis.