I guess you sent a small amount of BTC, 20% is probably the transaction fees you payed to send the coins. The transaction fees are really hight for BTC now I think it is around 15 to 30 USD or so. Better to send LTC or ETH for small amount of money and then convert back to BTC. In any case these fees are not related to COINBASE.
PS: Avoid bittrex by the way, if your account is not verified you will not able to withdraw your coins. Verifying an account takes ages (for me still waiting since 2 weeks)