How did you measure the 1/8" drop in water level?
Bubbles coming up from the shower drain is very odd. Do you have pictures of the rough in work? Is the shower connected to a P-Trap?
1/8" of water is a lot. I would re-test and use a proper plug.
There should be no water after a leak test if the drain is installed properly and the drain has weep holes.
Can you post a picture of this drain?