If I am reading your question correctly, an appraisal has been done on the property ("the bank wants $24,000 ... above the Appraisal"). If this is correct, and the property did not appraise for the amount the Short Sale Lender ("SSL") is requesting, then the SSL needs to be made aware of this.
In my experience, if I have a bona fide appraisal below the SSL approval amount, the SSL will reduce their approved price to the appraised price. They realize that if they go through the foreclosure process and then have to sell the home themselves as an REO they will find it difficult, if not impossible, to sell the property for more than the appraised value.
Have your agent write an addendum to the purchase contract indicating that you are willing to pay the appraised value, per the attached appraisal. Then have your agent request that the listing agent present this addendum (with the attached appraisal) to the short sale lender for their consideration and approval. Of course, if the SSL has a higher appraisal, then ask that they show their appraisal to you and then have an appraisal review done by either or both appraisers to settle the difference.
SSLs are already losing a significant amount of money on most short sales. They want to make sure that they are not letting the house go for significantly under market value. An appraisal is one tool by which to determine market value. Get the information to the SSL so they can make an informed decision and Dare to Dream.
Shel-lee Davis, CDPE, SFR, QSC
Your Real Estate Consultant for Life
RE/MAX Palos Verdes Realty