How soon can you buy a house after a short sale and bankruptcy?

This question is slightly more complicated than one may think. The answer depends on many things involved in both the bankruptcy and short-sale. Currently most lenders consider a short-sale the same way they consider a foreclosure, so you're stuck waiting 3, 4, or even 7 years before you can buy again. That being said, the FHA will allow you to buy a home again with no waiting period if you were able to short-sale your home without ever falling 30-day+ behind on your mortgage payments. That being said, we all know that many mortgage companies won't even entertain a short-sale unless you fall 60, 90, or 120 days behind on your payments. In the off-chance that you were able to successfully short-sale your home without ever falling behind on the payments, then we can go on to the bankruptcy portion of your question.
Bankruptcies are treated differently depending if they are a chapter 7, chapter 13, or less commonly a chapter 11. A chapter 7 BK is a liquidation of debts with no payback. A chapter 13 allows you to roll-in the arrearages you owe on the mortgage, and get back on track but requires a payback period for all or a portion of the debt. This is naturally the option people choose when looking to file bankruptcy and save their home. The guidelines about getting a new loan after bankruptcy, again, vary depending on the lender and the loan program... but generally you're stuck waiting 2, 3, or 4 years from the DISCHARGE date of the bankruptcy. This of course assumes that by that time your credit has rebuilt enough to qualify (must be a 620 or 640 with most lenders nowadays).

Lastly, if you haven't had a flawless payment history on the debts on your credit report since bankruptcy, it is very unlikely that a lender will entertain a home purchase for you regardless of your actual credit score.