i think they should help you, if they can.
your bittrex account was created before bch fork?
No sadly it was only created around a week ago, I am still very new to this.
bittrex most probably dont own the address you sent to.
sorry, i dont think you will be able to recover it.
if youre not able to recover thru bittrex, i suggest you post the address here.
Since the amount isn't worth $5000 USD and it's certainly not worth their 0.1BTC fee, it looks like it's gone unless a miracle happens and it doesn't get confirmed eventually.
Lesson learned the hard way.