In those links, the Taliban wasn't offering to hand Bin Laden over to the US, they were offering to hand him over to a third country that would never hand him over to the US. We can argue about whether Bush should have agreed to that offer, but it's a far cry from "refusing to take him":
> Afghanistan's deputy prime minister, Haji Abdul Kabir, told reporters that the Taliban would require evidence that Bin Laden was behind the September 11 terrorist attacks in the US.
> "If the Taliban is given evidence that Osama bin Laden is involved" and the bombing campaign stopped, "we would be ready to hand him over to a third country", Mr Kabir added.
> But it would have to be a state that would never "come under pressure from the United States", he said.
> In Jalalabad, deputy prime minister Haji Abdul Kabir - the third most powerful figure in the ruling Taliban regime - told reporters that the Taliban would require evidence that Bin Laden was behind the September 11 terrorist attacks in the US, but added: "we would be ready to hand him over to a third country".
> The offer came a day after the Taliban's supreme leader rebuffed Bush's "second chance" for the Islamic militia to surrender Bin Laden to the US.
> Mullah Mohammed Omar said there was no move to "hand anyone over".
That was a highly-conditional offer, that I suspect the U.S. administration felt was designed to give the Taliban and bin Laden breathing room to escape/hide/whatever their next move would have been.
Well thankfully we put a stop to that and immediately brought an end to the conflict and captured Osama without billions of dollars and a potential war!
* https://www.theguardian.com/world/2001/oct/14/afghanistan.te...
* https://abcnews.go.com/International/story?id=80482&page=1