If you get bullfrogged on a server with whirlpool as its first ice, do you get whirlpooled?

If your question is is being bullfrogged after hitting whirlpool allows you to jack out then no you still can not jack out even after you've been bullfrogged since the run is still going on. If your question is after you get bullfrogged and moved to a server where the next piece of ice is whirpool, you have the opportunity to jack out before approaching the next ice. If you don't, then the run proceeds as normal.

The Bullfrog subroutine, if successful, only moves the runner such that they are now running on a different server.

The run is still ongoing so any previous subroutine effects such as R.S.V.P or Whirlpool will still apply. Similarly, the rules preventing jacking out on a server only apply to the first piece of ICE approached each run, so just because Whirlpool may have been the outermost piece of ICE on the new server, the Runner can still choose to jack out if they so wish (as they will have already at least approached and encountered the Bullfrog before it).