I am attempting my first Bitcoin transfer from Abra to Bittrex. I am only sending the equivalent of $10 US dollars to test it. The money did not go through as I do not have enough in my account to pay the fee which is $44!! Is this right - it costs $44 USD in fees to send $10 USD?
Yes. The price of transactions fees in Bitcoin are not a percentage of the amount you are sending, they are formed from a market process and influenced by their size in bytes.
As there is a limited amount of space in each block, all users are currently bidding against each other for space in the blocks. As you can see here, the price of transaction fees has been bid up to approximately what you described.