Yep, the homeowner still owns the home, not the bank in a short-sale situation. So the homeowner and his/her agent selects the most viable offer to send to the bank for approval. What this means is that the homeowner is the only one that can legally ACCEPT an offer as he/she is the legal owner of the property. To accept an offer, the homeowner's agent (listing agent) will analyse the offeror's offered price, down-payment, deposit, credit scores, proof of funds (bank statements, 401K statements, CDs, etc), percentage of loan for the loan type (eg 80% loan for a conventional loan), then the listing agent will also analyse the property value to ensure that the offerred amounts will appraise (thus if an offerror overbid significantly, that offer may not be accepted if the listing agent feels it will not appraise); then the listing agent will interview the buyer's agents to determine which buyer will stick with the sometimes lengthy short-sale process and not flake out. Based on all of the above, the owner in consultation with his/her listing agent will select the most viable offer to officially accept and then send that accepted offer to the bank(s) for approval of the shortsale.
Thus to answer your question specifically, the owner (in consultation with his/her listing agent), not the bank negotiator selects the offer.