How many illusions will Lightning Bolt and Wild Ricochet get rid of?
603.1. Triggered abilities have a trigger condition and an effect. They are written as "[Trigger condition], [effect]," and begin with
  the word "when," "whenever," or "at." They can also be expressed as
  "[When/Whenever/At] [trigger event], [effect]."


The bear's ability is a triggered ability.


  603.3. Once an ability has triggered, its controller puts it on the stack as an object that's not a card the next time a player would
  receive priority. See rule 116, "Timing and Priority." The ability
  becomes the topmost object on the stack. It has the text of the
  ability that created it, and no other characteristics. It remains on
  the stack until it's countered, it resolves, a rule causes it to be
  removed from the stack, or an effect moves it elsewhere.


After you cast the lightning bolt, you are a player and you get priority, bear A's sacrifice ability is put on the stack. You still have priority. You cast the ricochet.

So the stack looks like this:


Wild Ricochet
BearA Sacrifice
Lightning Bolt


Then if everyone passes, wild ricochet resolves. As it resolves you choose to target bears B and C.

Now the stack looks like this:


BearB/C Sacrifice
BearB/C Sacrifice
(copy) Lightning Bolt
BearA Sacrifice
Lightning Bolt


If all players pass priority after each ability resolves then the bears would be sacrificed in the order you see on the stack.

Between each sacrifice ability resolving, priority passes and players can add to the top of the stack.

So yes all three are sacrificed, and none of them are actually dealt any damage.