I'm quite sure OP is referring to NEO which before the name change was called AntShares. OP probably hasn't had access to his account for a loooong time considering that he still refers to them like that.

I personally am not a fan of exchange to exchange transfers because when something goes wrong and the coins get sent back, they go back to the exchange's address they were sent from, and not your deposit address.

Best thing to do is to download a client such as Coinomi that supports plenty of altcoins-- send them to your Coinomi wallet from Bittrex, and from there to Binance. It's not even very time consuming.