Is there any exchange where I can place some money on the books, and short sell Bitcoin?
I think Poloniex may have that feature. I used Poloniex a couple of years ago and they had margin trading but I never used that. I cant say for sure if it included short selling or if it was just buying on margin.
Another option is shorting using a Bitcoin ETF. I think there are a couple of exchange traded funds through regular stock market trading available.