How can you be a BEAR in a market where you cannot establish a short position?
Your either BUYING to OPEN (BULL) or SELLING to CLOSE (NEUTRAL). No market I have seen allows you to SELL to OPEN (BEAR). If you cannot SELL which you do not own you cannot SHORT, if you cannot sell SHORT you cannot be a BEAR!! Of course in the world of ALT COINS you can also 'mine to open' but since your a net holder of the underlying (coins) your technically LONG making you a BULL.
A BEAR in true terms sells first to open a position and buys back to close a position hopefully at a lower price so he can profit. If he buys back at a higher price he takes a loss.
Being short or long is about the trade/position you take. Being bear is about the opinion you have. So yes you can be bear on a market that cannot be shorted. It just means that in your opinion the price of the asset will go down.
For example you can even say a news is bearish for a market and as far as I know, news dont put on trades : people do.