Are there any disadvantages because of the little air bubbles...annoying noises like bubbling...or do you have a lower cooling efficiency?
If not, try again the configuration with the inlet fitting on the bottom and let the system settle down over time.
The little bubbles really need only time to dissolve, they will disappear after some time for sure, but not just after a few days.
Just be patient, it will work. The drawing below shows, that the bubbles probably just circle constantly past the reservoir.
The reservoir is just a supplier for 'spare' water and not a catch tank.
There is no direct flow into the reservoir and the bubbles don't get into direct contact with the water-to-air surface.
That's the reason, in my opinion, why the bubbles need much more time to dissolve.