The Bounty system was never formalized, but informally, as the bounty initiator, you would be setting the terms. A few options:

1. artists comment indicating their interest and a link to their portfolio, then you would select the one you feel best fits the request. Once they finish the request, you pay them via paypal or whatever payment scheme you and the artist prefer. This method allows artists to be more secure about the bounty since only the artist who will get paid will need to perform the work. On the other hand, the bounty poster may not like the final product but has few options to go with a different artist once one is selected.
2. Artists perform the work and create the art (or parts of it, proof of concepts, etc.) before anyone is selected. The bounty poster then selects the art (or partial art) that seems to fit the requirements best. The selected artist completes the art and is paid via paypal or whatever payment scheme you and the artist prefer. This gives the bounty poster more security in being able to see what the final product will look like before selecting the artist. On the other hand, the artists may be performing work without getting paid for it if they are not the artist selected.
3. If the request is general enough, it could be useful to more than just one requestor, so many people may contribute to the bounty. This will increase the bounty and attract more artists and collaboration. On the other hand, individual requestors may want very specific details that are not compatible with the needs of other requestors. By opening the bounty to multiple requestors, you may have to forego some specifics so that the asset is useful to everyone.

There is no formal payment system in place. Just a paypal transfer, typically. In the past, payment was based on the honor system. If you promise to pay an artist for meeting the requirements, but don't like the result even if it meets the requirements, you're honor-bound to pay the artist anyway. If an artist shows a proof-of-concept or portfolio that implies a certain level of quality and style, the artist is honor-bound to deliver on a quality final product even if it is taking longer than expected and my no longer be worth the bounty offered. These situations are unlikely, but they should be considered when posting or fulfilling a bounty.

If an honor-based system of bounty and trade seems... unappealing to some, I can act as an escrow and arbitrator. Ultimately, you'll be placing your trust in me, though. At the conclusion of the request, I will do my best to weigh the situation fairly and without bias and determine if the artist acted in good faith or if the payment should be returned to the bounty poster.

As for determining price point, there's really no easy way to determine a decent market price other than talking to multiple artists or perhaps a bidding system. different artists have different rates, styles, and levels of quality. I am wondering if it may work to simply post (detailed) requirements for the asset, and encourage artists to post how much they would be willing to take for performing the task.

Does anyone else have some suggestions on how to handle this?

@um: consent has already been given for everything on this site :) https://opengameart.org/content/faq#q-how-to-credit

that's a good idea. I could add a preview sheet if anyone is willing to create one. :)

The mirrored universe idea seems pretty inspiring to me. As for the left-handed implication that comes with it, I'd specify we're looking for truly left-handed assets where a simple horizontal flip of a right-handed asset doesn't really produce the desired result. I guess that's what Cougarmint was saying. Does a mirrored universe theme seem too unfocused to represent both the "sinister/unusual" and "southpaw" ideas?