Hmmmmmm, well now we've got problems.. however that wasn't in vain, at least we now know there is indeed a problem.
One easy thing to check.. are the inlets on the bumper clogged? Some cars are finicky, on my Aurora when I moved the license plate so it covered a little bit of the opening it ran at like 230!! Moved the plate at it cooled right down. Check that first, maybe you hit a plastic bag or something silly.
How many miles are on the water pump?? Once in a great while the impeller completely gives out.. corrodes away, etc. If it's quite old that's something to change, just in case (can't really know until it's off if it's bad, sadly)
Also, no air getting into the system? I know you bled it a lot, but go bleed it a couple days later.. is it still OK or are there more bubbles? Does it lose coolant? Look under the oil cap, is it muddy in there by any chance?
Get a cooling system pressurizer tool (fits onto the overflow tank and you can pump it up to 15psi) and pressurize your cooling system. Does it hold? If so, good, you know the headgaskets, LIMG, and all other seals are OK. If it doesn't hold , time to find out what's leaking and where!
There's
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