Bayliss said Stokes, who will miss the Twenty20 game against the Kiwis on Sunday, needs to get back up to speed before he can feature in the starting 11.
"He hasn't played for a while," Bayliss told reporters. "It is not as if we can maybe bring him straight back for these T20s, for example.
"We have got to get him up to speed and hopefully during this one-day series we can get him back into the team.
"At this stage I'd have to say it was unlikely (he'll play the first ODI). We'll have to wait and see how he is with travel, with practice."
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Stokes, one of world cricket's most destructive batsmen, last played a competitive match for Canterbury in New Zealand's domestic T20 competition last December.
His absence was not necessarily felt during England's 4-1 ODI series win against Australia. However, that success has been followed by three consecutive T20 failures, with two losses against Australia and on Tuesday against New Zealand.
"Right throughout the summer we've been down to five bowlers, especially in the one-dayers and T20s," Bayliss added.
"We've been able to have six bowlers before, which gives the captain plenty of different options. I think that's what we've missed the most apart from his individual performances."
Stokes is expected to feature in England's two tests against New Zealand at Auckland and Christchurch next month.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
