Is anyone the "captain" of the partnership after the following bidding sequence?
For the most part, in Bergen, the opener is the &quot;Captain&quot;.  Responder does what Opener tells them to, nothing more.  This is particularly true here, in the 1S-3S sequence, which is often described as &quot;preemptive&quot; - it describes a weak hand.
The way you can tell is how the response is very tailored to provide fairly specific information, and then the rebid from opener is either signoff (including pass), or (to lower 3-level responses) includes the help suit game try, which is still fairly limiting in the options it provides.  Opener could have almost any hand (could be 12 HCP, 5-3-3-2, could be 18 HCP, 5-3-4-1, could be 11 HCP, 6-4-2-1, etc.)
Most of the time in this auction, opener passes or raises to 4S (if opener is particularly strong, particularly shapely, or in competition if opener has a 6 card suit or is otherwise willing to tolerate 4S competitively).  Since opener didn't open 2C, you're out of slam territory excepting very limited situations, and so the standard Bergen sequence such as described here doesn't usually mention any other options.
More generally, when you see a conventional sequence, you can tell who is captain because that's the &quot;asking&quot; hand.  The asker is captain, deciding what the ultimate contract is, and the responder just answers questions. Often conventions are structured so that the eventual declarer is captain - because that way defense finds out the least information possible about that hand - but not that's always possible.
There are cases where it's handed off - like in the sequence




S
W
N
E




1S
P
3C
P


3H
P
?





There, South has made a help suit game try, and is giving control to North - asking if North thinks 4S is worth considering.