The Earth should probably be cooling, at least, that's what the Milankovich cycles and historical variation and recent temperature charts all indicate.
See XKCD and related question on XKCD chart, and temperature chart over the last 800,000 years. Source.
Now, it should be pointed out that the Milankovich cycles don't line up in perfect synchronicity, so no two warm periods and no two ice ages should be exactly alike, but there are similarities, like a steady cooling after a warm period. Earth has been gradually cooling for roughly the last 7,000 years, and this is due to the gradual changes in the Earth's orbit per XKCD. (scroll to 5,000 bce - see note).
If Earth cooled 1°C in 6,500 years and is due to cool 4°C in the next 10-30,000 years as the next ice age comes along, we can ballpark estimate 1 degree of cooling per 5,000 years, and if we use an estimate of 2 degrees warming by 2,100 and climate change took hold in the 1980s, that's 1 degree every 60 years current rate of warming.
So, by my estimate, man is responsible for 101% of the current warming and Earth's natural cycles are shaving about 1% off man made climate change. To say it's all us is accurate enough for me. There's currently no natural warming of the Earth as far as I can tell, Earth should be cooling. Granted there's variation, like the current solar cycle is a few tenths of a degree warmer than the maunder minimum that is believed to be the cause of the little ice age and our relative lack of major volcanic activity for much of this century might have a slight warming effect, so precise numbers are hard to pin down, but I think 101% man, -1% natural is pretty close to accurate.
That part of the video begins about 2 minutes in, goes on for about 3 minutes, then it moves onto "how would the Earth be different"
If I may rant, there's several things I don't like about the interview.
Tucker Carson says 1:18 "The essence of science is extreme skepticism" - that just ain't so. Skeptisism doesn't equal scientific discovery. Bart Simpson is a skeptic - I don't think we should listen to his views on science. Skeptisism is important to science but it is absolutely NOT the essence of science. The essence of science is asking the right question and working out an answer through evidence and testing and peer review. Peer review doesn't mean denial. For Peer review to be meaningful, evidence or solid counter argument must be presented - not just empty skepticism. Skepticism that ignores the evidence is about as valuable as a restaurant that doesn't serve any food. Skeptics must respect and understand the evidence if they are going to provide intelligent skeptical arguments on why the evidence might mean something else. If they don't do that, it's just noise. Intelligent skepticism that respects the evidence and data is always welcome. Uneducated skepticism is a pointless and senseless distraction. It's like trying to form sentences without using any words.
But try explaining that to a skeptic sometime who thinks he doesn't need to be educated because skepticism is his education.
Tucker then says, about 1:50 "the climate has always changed" - again, not really. There are periods of what might be called climate consistency and periods of climate change. The climate isn't "always" changing, but it does change fairly frequently. There's also some clarity on what constitutes a change - weather changes during the seasons, but that's not climate, not really. Climate incorporates the seasons and year to year variations. Real climate change, by my definition, happens every few thousand years - give or take, and big changes, with the current ice age cycle on a 100,000 year time-frame, big changes happen twice every 100,000 years, with the rise and fall of ice ages. There's some room for opinion in this though, but "always changing", a common phrase by deniers - but simply not accurate, not if you're talking about real change. Now if you're talking about irrelevant change then, sure.
Pretty much everything is always changing. A human's height changes about 1/2 inch from when they wake up to when they go to bed, A human in space grows a full inch, but, . . . I still say I'm 5'10 when asked and I'd say I'm 5'10 if I lived on the space station. I don't say 5"10 1/2 cause I just woke up. Even though my height is always changing depending on how long I've been standing up, 5'10 is close enough. Relevant, significant change is worth identifying. Incidental or irrelevant change based on fluctuations that go back and forth mostly doesn't need to be identified.
So, no, the CLIMATE is NOT always changing. Weather is always changing, climate goes through periods of decades, centuries, sometimes Millennia, where it remains consistent enough that we can say it isn't changing. "The climate is always changing" is a red herring.
Everything Bill said is true, though I wasn't crazy about his initial time scales "change used to happen over millions of years" and "now it happens over decades and years" - that's iffy, but mostly everything he said was true, but he didn't handle the interview very well. Tucker's Gish Gallop was successful.
When Tucker moves onto "how would the Earth be different", Bill does answer him with specifics, but Tucker just pretends those aren't good answers and interrupts Bill or goes back to the first question when he doesn't like that his 2nd question is being answered. Overall it's a terrible interview designed to sell disinformation, not inform. Painful to watch and I hate Fox News for that reason.
OK, rant finished.
There's no right answer. 101% - by my estimate. 100% if you believe the Earth isn't getting cooler. 102% or more if you set the rate of cooling a little higher, with the next ice age due in 10,000 years not 20,000 years. (as of now, the next ice age is on indefinite delay - but that's another story).
Or, the answer could be, 70-90% if you believe there's an un-accounted for natural warming period over the last 30-40 years. That's one of Judith Curry's arguments that climate change has gotten a natural push to make it look bigger than it is, but, she has no good proof, which is why she's mostly alone in that argument. It's just something she's claiming.
100% is a good answer too, and if you listen, Bill does say 100% at one point, but it's during an interruption and hard to hear. "We aren't sure but close to 100% is also a good answer".
If Tucker had asked me what percentage. I'd have showed him XKCD's chart and said "see this point here, the cooling began shortly after 5,000 BCE, at a rate about 100 times slower than the current warming. 101% is relatively consistent with past Milankovich cycles and past periods of cooling following a warm period between ice ages. So, that's my answer. 101% of the current warming is man-made.