During my opponent's declare attackers step, I gain control of Grizzly Bears using an instant. May I use it to block during the declare blockers step?
Different situation: My opponent blocks my Grizzly Bears with their Hill Giant, I use an instant speed effect that gives me control of my Grizzly Bears. Does it survive combat?
If you control the creature when declaring blockers, the creature can block as normal. If something else prevents it from blocking (such as being tapped, though I'm not seeing any mention of the Grizzly bears being tapped in the question), it won't be able to, of course.
Changing control means it goes from one controller to another. If the same person controls it continuously, then control never changes. Also note this has nothing to do with who the owner is. "Owner" and "controller" are two different things, though often are the same person. The controller of an object can change, the owner cannot (excepting ante)