How can I do this better? To whom to address? To the project manager? If so, how does bounty advertising work, who develops banner design
Yes, you should contact and hire a campaign manager. Banners are designed by designers here (normally) and for some cases, there's an escrow provider (for reputable managers, they're the one to handle the payments instead).
But I would like to know the main features of connecting advertising with the bounty to the site.
Since you're somehow new, take a look at the following websites (they'll be the one to help and do most of the tasks):
1.
Bounty Portals2.
BountyHive3.
BountiesAlert4.
BOUNTYPLATFORM