I've only ever done car brakes and (especially) clutches. My recollection is that there was a gradual deterioration from perfect, to ok, to could be better, to no worky. Hard to say how much air came out because you'd initially get a load of bubbles from your rubber pipe dipped into your jar of brake fluid. Tended to keep flushing through till the tiny bubbles stopped.
Edit: Do push bike brakes even have bleed nipples, or do you have to do the syringy thing you mention - which does sound rather tricky
Yes, they have bleed nipples. Some of them have grub screws in ports. You remove the grub screw and screw in a nipple.
Bleeding is not like in a car. You just open the port/nipple on the caliper, remove the lid on the reservoir at the handlebar and squeeze fluid in from the bottom. No pumping required. IIRC, the entire system has something like only 15ml of fluid in it. We use transparent plastic syringes with transparent silicone tubing. We can see bubbles go in because you cannot not get air in when you start. However, this air is out the top within 5 or 10ml of fluid being pushed in. If it is a Shimano system, this is good to go - no internal traps. If it is Elixir, you can fiddle for days to get the bubbles out.
When you bleed a system with an open reservoir like Shimano or Hayes or Hope, you can see into the reservoir and observe what comes out. That's when you can see the micro bubble escaping and you know your problems are over.
Older brakes and absolute rubbish brakes such as Avid Elixir, are full of bubble traps. Thankfully the last few years saw a huge improvement in internal cavity design so that you don't have to tap like hell with a screwdriver to try and dislodge bubbles nor do the bleed process in all sorts of angles.
The bubbles that make the difference are too small to float to the top by themselves. In other words, the difference in density is smaller than the fluid's viscosity and even should you hang the caliper straight down by its hose and shake it, the bubbles won't float to the top.
Two things have puzzled me over the years and I have not had anybody to help me solve the problem.
1) Why does such a small bubble make such a big difference. You posed this question again and in all my years of training mechanics, none have ever asked me that question. It is kinda good 'cause I don't know the answer.
2) Why does pumping the lever temporarily harden up the system? Where does that bubble go when you pump? I wish I had a transparent brake assembly and can fill it with various coloured liquids and just observe.
