Here's what I do once in a while for my Shimano hydraulics:
I don't have a Shimano bleed kit, and I don't plan to get one because this works good enough.
So when a bike is upside-down for a while, and you right-side it and want to ride, the brake levers need a lot of pumping until they work. Does that mean there's more air up at the lever, or down at the caliper (which used to be 'up' when the bike was upside down)?
Would a burp or 'lever bleed' be more quick/effective if you upside down the bike for a few hours first?