No, if you don't move coins, then you don't need to do anything.
Can I move my bytes to a new wallet now and still get my blackbyte bonus ?
Yes. Remember to move both types of balls to your new wallet. Or, simply don't move them at all unless there is a specific reason.
So If I moved the byteball coins to Bittrex from my registered btc address, then I won't get byteball in the next distribution? so it is necessary to do a new registration of the same btc wallet that was used/registered before?
edit: (below is related to bitcoin address as I first misread your question)
Correct. You don't get any byteball from a BTC address that has a 0 (zero) balance. 0 x 0.0625 = 0
You will get the 20% bonus to your account for the byteball you have though.
No, it is not necessary to do a new registration if you simply move your bitcoin back to the registered bitcoin address. Just make sure you move it in time so that the coins are confirmed prior to the distribution. I have confirmed with 100% certainty that an address with unconfirmed coins do not byteball which is a good thing. (Just imagine how many people would try double spends to a bunch of addresses trying to get double byteball.)
update to my response after I realized what you were asking....
Just realized you asked about moving your byteball from the registered address.....
Byteball (as far as I understand it) are all getting the bonus - not simply the ones in the registered 'bitcoin' linked accounts.