If they (bittrex) import the private key that was used to generate the BSV address into a BTC wallet, they'll be able to give you a partial refund (it would be acceptable if they charged you a couple hundred bucks to pay their engineer to perform these steps).

~~
. Some exchanges do this for free, others charge a nominal fee, some won't help you at all... It's a roll of the dice, but if i were faced with this situation, at least i'd try to get my funds back.

Bittrex will attempt to recover funds which fall under three scenarios.
Crosschain Deposits
Removed Wallet Token Recovery
Unsupported ERC20 Token Recovery

Not all deposits can be recovered and the time frame of recovery is at our discretion.

Please allow up to 30 days for recovery once payment has been received and confirmed.

Crosschain Deposit Recovery
Crosschain - A deposit of one coin to a different coins address is considered a crosschain deposit

Bittrex will only attempt to recover crosschain deposits that exceed $5000 at the time of deposit, within 7 days of the deposit and will charge a 0.1 BTC for this recovery. Recovering coins crosschain is an inherently dangerous and time consuming process.

Due to our new Crosschain Recovery System, the minimum requirement for crosschain recoveries is $3000 at the time of deposit for the following crosschain pairs:

BTC to BCH
BCH to BTC
BTC to USDT
USDT to BTC