Sorry for the spam. I see I made a typo in the timeit script. Next time I will be more dilligent when making these kinds of reports and triple checking it before hand, and sending it once. I used -c instead of -s and now all the setup time is also included. This confounds the results.

The proper test commands should be:

python -m timeit -s "from bytes_sort import bytes_sort, bytearray_sort_inplace" "bytes_sort(b'My string here')"

python -m timeit "bytes(sorted(b'My string here'))"

Using just sorted, to purely compare the sorting algorithms without the overhead of creating a new bytes object.
python -m timeit "sorted(b'My string here')"

Correct comparison results
# String = b''
using bytes(sorted: 188 nsec
using sorted:       108 nsec
using byte_sort:    125 nsec  # Some overhead here, setting up the countarray
# String = b'abc'
using bytes(sorted: 252 nsec
using sorted:       145 nsec
using byte_sort:    136 nsec  # Overhead compared to sorted already negated when sorting 3 items(!)
# String = b'Let\'s test a proper string now. One that has some value to be sorted.'
using bytes(sorted: 1830 nsec (reported as 1.83 usec)
using sorted:       1550 nsec (reported as 1.55 usec)
using byte_sort:     220 nsec