What does "bob and weave" mean?
Picture a boxing match. The moves that one boxer does to avoid the punches of the man trying to hit him (ducking down, stepping aside, leaning one way or the other, etc.) is an an example of "bobbing and weaving."
As an idiom, bob and weave means to be obviously evasive.
When the reporters asked the politician about his extra-marital affairs, he did a lot of bobbing and weaving, but he never answered their questions directly.
One does not bob and weave through a crowd. Bobbing is, as Ouisch said, "ducking down," and one would not do that in a crowd. One would, however, weave through a crowd.