Shorting requires that you borrow the stock/commodity/currency/whatever from someone else who owns it, and then sell it on the open market. The borrowing usually entails interest. That is, someone might be willing to lend you the bitcoin so you can then sell them (the short), but that person is also going to charge you, say, 5% of the bitcoins lent payable in bitcoin or some other stock or currency each year as long as they are borrowed. At some point you have to buy the bitcoin back to pay back the person you borrowed them from.
Another problem is that borrowing any significant quantity of anything, such as bitcoin or a stock or whatever, requires a trusted and/or regulated middle-man who can guarantee that the lender gets paid back and consequences if you are unable to pay-back the middleman. Otherwise only a fool would lend you the bitcoin with only your 'promise' that you'll pay him back. This is how shorting in the real stock market works.
Lots of ways to blow yourself up. Usually the lender can call back his or her stock/bitcoin/whatever with less than a week's notice, which might force you to buy-back the bitcoin you sold at a loss if you can't find someone else to borrow the bitcoin from. The lender and/or middleman (aka your broker in the case of stock) also needs to protect themselves, and so there will be wording that requires you to maintain a balance sufficient to buy back the bitcoin you owe them. So if the price of bitcoin were to double and you don't have sufficient funds to cover the value, they can force you buy back the bitcoin right then and there to pay back the loan. Just two examples.
So I'm sure there would be someone willing to lend you the bitcoins, but if they do they are going to be asking for your first born child and your house if you can't pay them back, and probably charge you 20%+ in interest in the mean time.