Actually Bitbay was at Bittrex and now is just being delisted. Just log in at Bittrex and you'll still find BTC/BAY pair there (frozen) and BAY wallet.
So, let's handle OP's problems.
1. Where to move the funds, that's up to you. If you find a good exchange move there, else you'll have to use the official wallet for Bitbay, which you have to install and get an address.
Others already said about Nova Exchange, I see even BitBay team tweeted about it:
https://twitter.com/BitBayofficial/status/1162625079580254209If you want to transfer to another exchange, you can do it directly, just go there and generate a new Bitbay address for yourself.
Tell us which path you'll continue on and ask for more help if needed.
2. When you have the new address, go to
https://international.bittrex.com/balance and filter for Bay. You'll see then a green sign and a red sign before the Bitbay name. Click the red one, it's for withdrawals.
Fill the (new) address where to send to, fill the amount (you can test first with a small amount to make sure all is good), press withdraw. Depending on your security settings you may have to do other steps too (2FA, confirmation mail, whatever).
And wait. Because Bittrex may not send the funds out in the next second and because the recipient, if it's an exchange, will wait a good number of confirmations until it funds the account (but it may show the current number of confirmations). I didn't work with NovaExchange in the last 2 years, so I can't tell how it behaves now.
