Dispenser B can be activated by an adjacent powered dispenser A if dispenser B has a water bucket, but not with an empty bucket.

In the first screenshot are 2 dispensers each containing a water bucket in the top left slot. Pushing the attached button first powers the left side dispenser (dispenser A) then the right side (dispenser B) at which point screenshot 2 shows each dispenser with a water source block in front of it, containing empty buckets in each. Pressing the button again powers dispenser A but not dispenser B, leaving 1 water source block in front of dispenser B. At that point, dispenser A contains a water bucket and dispenser B contains an empty bucket.