He said that the ruling came as a complete surprise to the International Olympic Committee (IOC).
"We would never have expected this," Bach told a press conference in Pyeongchang just five days ahead of the opening of the Winter Olympic Games.
The IOC's disciplinary commission banned 43 Russian athletes for life and disqualified all Russians from competing at the Pyeongchang Games over a state-sponsored doping conspiracy.
It later ruled that 169 athletes who had proved they were clean would be allowed to compete.
Bach said that Olympic officials had asked CAS for an explanation for their ruling and had been told no full accounting would be released until the end of February.
The Games in South Korea end on February 25.
He said the IOC knew only what had been released by CAS in a press statement and this was "extremely unsatisfactory given the gravity of the cases".
On Saturday, the IOC said that 13 of the 28 athletes cleared by CAS would be considered by a special IOC panel for a possible invitation to take part in the Pyeongchang Olympics.
But Bach said: "The absence of sanctions by CAS does not mean that you are entitled to receive an invitation from the IOC because receiving this invitation is a privilege of clean Russian athletes.
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