I did check coinbase fees but it's near impossible to get an estimate on how much it will cost. I know the bitcoin must be converted to a fiat currency my bank accepts. That's the first puzzle. Which one?
You don't know which fiat currency your bank accepts? If you are on the US, you use USD; if you are on (most) part of Europe, you use EUR. What's so difficulty about it?
You clearly made a mistake somewhere since you lost half of your $50 withdrawal amount without even knowing where it went. That's not anyone's fault but yours. I'm sure you can Google "exchange X bank withdrawal fees" and you'll get a clear answer.
Coinbase, for example, charges 1.49% for US bank accounts (after waiver) and free through SEPA for European banks. Not that costy, huh?
Moreover, if the exchange charges a fixed fee per withdrawal regardless of the amount, then it may not be the best idea to withdrawal a mere $50. I can't know if that's what happened to you, but it's a possibility.