We don't know what kind of discussions Bruce Lee had with Ted Ashley about The Warrior. But we can agree it must have been a separate but similar idea to Ed Spielman's. Perhaps Warner Bros optioned Bruce's story idea and promised to pay him for it. Or maybe Bruce acted as a consultant on Ed Spielman's project. But then why would Bruce be referring to Ed Spielman's Kung Fu idea as 'The Warrior'? (Maybe that's just what Bruce personally called it?). I haven't come across any evidence that Kung Fu was originally called The Warrior.
We do know that director Jerry Thorpe really wanted Bruce to play the role of Caine. And so did producer Harvey Frand. But after Bruce met with Tom Kuhn (V.P. of Warner Brothers Television). Kuhn didn't think Bruce would be a good fit.
This is a video on the development and making of the Kung Fu TV series: