To me, this aspect of the Liberty is the worst part I have encountered so far with my 2007. I think my biggest issue leading up to this was I could not get my bleed screw out of the upper goose neck. Every time besides the last time I would have to back it off a bank to finish filling and bleeding it, which was a whole process.
This last time though I was able to get that bleed screw out no problem. I don't know if it was factory or 1st service... but mine had red loctite is why I couldn't get it loose. And I probably worked that stuff loose over time and by nearly overheating trying to bleed air out.
For me the trick after a flush is now I just put a small funnel in that bleeder and I start by filling the engine from there. This seems to push the air right out. Then I fill up the radiator, fire it up, make sure it is all good to go. It was also helpful that last time I caught and measured every bit that came out of the system. So I knew what had to go back in, and I had very little trouble getting it done this time around.