Unfortunately, at this time, we do not offer this functionality. On a Sharetribe marketplace, the price needs to be fixed.
Some marketplaces have used the comment section for the listings as a workaround. Users give their bids as comments, and when the bidding is over, the seller contacts the winning user. The seller changes the listing price to the winner's bid and only accepts a transaction from the winning user.
If the bidding is silent, the direct message system can be used.