Your best bet is to once again contact the exchange and Genesis mining. Provide the details of the transaction. Assuming you followed directions then Bittrex likely received the funds and doesn't know where to forward them.

You aren't the first person to loose some coin and you won't be the last. Very often there is no undo button. The best practices are:

1. confirm all details before transferring. Validate the first and last 4 to 6 character of the addresses even if they were copy and pasted.

2. Send a small amount first and only send more once you have confirmed it has arrived.

3. Use a notepad application to record all of the transaction details. This way, if there is an error, you can provide them to support or use block explorer sites to find the transaction.

Likely, Bittrex support will be able to help so long as you can provide all of the transaction details and the payment was actually received by them.

In my opinion, banks aren't better. When you deposit your money, you no longer own it or have control over how it is used (same applies to leaving money on an exchange like bittrex, use the service and move that capital). I will take freedom over slavery, debt and crappy support/minor conveniences any day.

Last, who the hell is charging $100 transaction fees? Not even Bitcoin is doing that.