I stored my bitcoin in a Mycelium wallet on my phone during the fork.
To split the BTC and BCH I used the Electron cash wallet. I only trust it with my BCH so I first had to empty my BCT from the HD wallet.
You need to send the BTC to a different wallet because if you just make a new wallet in Mycelium it will still be the same seed.
I then imported the seed into the electron Cash wallet and send it all to Bittrex.

There is a privacy risk with emptying your complete wallet with one transaction because you will link all your addresses. If you prefer privacy you need to send each unspent amount separate.