"He told me he felt he had achieved the things that he was keen to achieve in the role and he said he was keen to pursue other opportunities."
She did not respond to questions about any exit package agreed to with Mr Bayliss.
Racing Minister Nathan Guy also avoided the question but issued a statement saying the minister had just 24 hours' notice Mr Bayliss was leaving.
He said he was told of the resignation on Monday but was aware discussions were under way. He said it would be "inappropriate for me to comment on what is an employment matter between the two parties".
NZ First leader Winston Peters, a former Racing Minister, said Mr Guy needed to spell out why Mr Bayliss was leaving.
"[Mr Guy] should be telling us exactly what happened. There are in excess of 35,000 people [in the racing industry] who have a serious interest in this answer."
He said Mr Bayliss was leaving a "critical role" in an industry which needed government support. "The minister is not taking responsibility."
Mr Bayliss was appointed in August 2012. The board oversees sport betting and racing in New Zealand, running the TAB and distributing profits to the industry.