The כל בו writes that when the חזן says 'ברכו את ה
he should bow down.
There is no mention in the כל בו that when the ציבור
answers ברוך ה' המבורך that they too should bow
The מגן גבורים writes that the Minhag of the Velt is for
the קהל to bow down at ברכו but there is no סמך
(source with a slight reason) for doing so.
Since in Shulchan Aruch (O.Ch.113:3), it is written
"שאין לכרוע אלא במקום שתקנו חכמים"
One may not bow only in those places where Chazal
instituted to do so.
The מגן גבורים is desperate to find a reason why it's
done at ברכו. He came up with a דוחק answer.
The ביאור הלכה is not happy with the דוחק answer
from the מגן גבורים and came up with his own סמך
The (ספר העתים (ר"י אברצילוני (one of the newly found
Rishonim. It was printed for the first time only about
100 years ago) writes that when the ש"ץ says ברכו
then the קהל should sit* "בכובד ראש ראשיהם כפופים"
(respectfully with their heads bent down.)
Perhaps the origin of this Minhag was not to bow down
but just keeping ראשיהם כפופים the way the ספר העתים writes
to sit with heads bent down. As time went on people
stood up and bowed down instead. Hence the Minhag
we have today of bowing down.
The מגן גבורים and even the Chofetz Chaim didn't see
the ספר העתים and therefore are desperate in finding
a reason for the קהל to bow down at ברכו.
The Magen Avraham (51:8)writes that it is possible that
the Halacha of not bowing is only while standing
and not while sitting.