This is the reality of JFK, there are no established airside connection routes between terminals. In at least the last 15 years or so the only airside connections I can recall are the Delta bus between T2 and T4 (now gone, along with T2), and the relatively short-lived AA/B6 bus I mentioned above.

BA becoming a codeshare partner of B6 (more or less forced on them since AA gave up some ex-JFK routes to B6 under the partnership, including MCO, and did not reinstate their own operation from JFK on all these routes after the partnership ended) is unlikely to produce anywhere near enough pax to justify operating this again, though of course nothing is impossible.

For the many years when BA was in JFK T7 and AA in T8, all BA<>AA connections required a landside terminal transfer, as many of us here can testify, and there were a lot more of those than there will be between BA and B6. Regrettably, unless that article I posted was wrong (which I doubt), you are looking at a landside connection. For clarity, on a single ticket any checked bags will be transferred airside on this connection, it's only you and hand luggage that will have to go landside. How long do you have between flights?