George Dobell is a senior correspondent at ESPNcricinfo
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Bairstow's maiden Test century in Cape Town, a fine innings of 150 not out that, in partnership with Ben Stokes, led England from a precarious to a dominant position, underlined his status as first-choice keeper in England's Test team.
While he did drop an important chance during the second Test, Bayliss believes that Bairstow's keeping will improve if he is given a run in the side and suggested that none of the other keepers vying for selection - notably Buttler - are significantly better with the gloves.
That leaves Buttler unlikely to be required for the early season Tests against Sri Lanka in May and June. With the England management keen to give their white-ball players more experience of other domestic T20 leagues, especially the IPL and the Big Bash, Buttler will then be free to appear in the IPL if he wins interest in the auction.
As things stand, it seems likely that he will gain interest from several franchises and, as ESPNcricinfo reported, Kolkata Knight Riders are particularly interested in signing him. The deadline to register for the IPL auction is January 15.
England made a similar decision recently with Adil Rashid. Although he remains part of their plans in all formats, the management concluded that he was unlikely to play a role in the Test series in South Africa so encouraged him to take part in the Big Bash instead. There, he has so far impressed with 10 wickets in five matches for Adelaide Strikers, including a Man of the Match performance against Perth Scorchers, that have helped propel his team towards the semi-finals.
The difference this time is that Buttler is being encouraged to play in the IPL (which this year runs from April 9 to May 29) during the England season. While fringe Test players have, in the past, been encouraged to remain in county cricket and fight for their places, the England management is currently taking a different view. Whether that is because they see Buttler as a white-ball specialist, or simply because they feel he will learn as much in the IPL as he would in the county championship, is unclear.
"If the opportunity arises and Buttler is not in the Test team and that IPL window is a possibility, I'd be all for it," Bayliss said.
"It's something we've spoken about. Personally I'd think it would be something similar along the lines of Adil Rashid.
"If Jos is in the Test team he'll be playing Test cricket for England. He definitely wants to play more Test cricket for England which is great. But obviously Jonny's there at the moment."
Bayliss suggested Bairstow had kept "pretty well" in Cape Town, but accepts that part of his game needs to improve. Bairstow only allowed through four byes in the entire South Africa innings - a decent effort given that England were in the field for 211 overs - but he did put down a relatively straightforward chance to his right off the bowling of Stuart Broad when Temba Bavuma had scored 77. He missed a similar chance in Durban, as well as missing stumpings in Durban and in the previous Test in Sharjah.
"Apart from that one chance I thought he did a pretty good job," Bayliss said. "He fumbled two balls and unfortunately one of them was a nick.
"Certainly his wicketkeeping is a work in progress, but I think our other wicketkeepers are as well. Plenty of other wicketkeepers around the world have started off their international careers not in the greatest fashion but ended up pretty decent keepers. It's only fairly early in Jonny's wicketkeeping career.
"He works very, very hard at it and I'd expect over a period of time for him to get better. Both Jonny and Jos work terribly hard on their keeping. I'd expect over a period of time for him to get better.
"He knows the number one reason he is in the team is to keep wicket. So that is definitely a focus of ours: to make him better, as it is with Jos as well.
"And we know that both of them, in form, can quite possibly play in this Test team as a batter anyway. So it's all in front of both of them."