what is main logic behind turning a register into byte count other than multiplying by 2

Answer :

In Bubble sort, we comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted.

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So basically we are using 2 counters, in complete sorting algorithm, One through which we are checking that whether are ended with list or not, Second through which we are checking either the specific item in list is sorted with respect to its neighbor or not. In our code, we use CX as a byte count in order to check that the algorithm is going through the complete list or not and SI for internal counting whether the specific item is compared/swapped with the remaining list or not.