It's probably not. I tried to extract the commit hash from the version of bun packaged in claude code. the commit hashes from previous versions resolve, whereas the commit hash for the current 1.4.0 isn't available.

from strings:

   bun-v1.4.0
   f6d0fcd24abd48061873c2f1a6fb2a67eee487b8
    Upgraded.
   Welcome to Bun's latest canary build!

(In contrast, earlier builds that I have locally have commit IDs that can be found in the public repo). I don't think it's particularly damning for them to vendor a canary release, mind you.