"I was having a laugh watching him in the field, running around in the covers," Bayliss told reporters.
"He looked like he was enjoying it. For someone at this stage of his career, that's a good sign."
Bayliss said Root was nervous before the match and compared the two captains' styles of communicating with the team.
"Before this test he (Root) was a little more on edge than I've seen him before," Bayliss said.
"We spoke about Joe being himself, getting the message across in his way.
"He's proactive and confident and I thought that came across in the way he led the team.
"Root and Cook are different characters, they go about their batting in different fashion, so the dressing room was a little different. A lot of the messages were similar, just delivered in a different way."
The second test starts on Friday at Trent Bridge in Nottingham.
(Reporting by Aditi Prakash in Bengaluru, editing by Ed Osmond)
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