Does Bittrex support short selling?
Nope. Margin trading is still not available on bittrex, so therefore you can only take on long positions with whatever money you have right now without any sort of add-on leverage. Just the way it is right now but they are planning on adding it in the future.
See this article:
https://support.bittrex.com/hc/en-us/articles/115000762772-Margin-Trading-AvailabilityYou can use poloniex/bitfinex for shortsells though.