I’m asking because while having a conversation with my American friend (I’m Canadian), we somehow got on the topic of nukes and WW2. He mentioned something about how Japan was lucky it was cloudy that day, which sparked me to ask what he meant. He said that he learned in his school that America had 3 nukes but they couldn’t drop the 3ed bomb because it was cloudy that day. I then replied saying that’s not at all what I learned in my school, that America only had 2 bombs and wouldn’t have a 3 one ready for at least a month, during which time they could have counter attacked. But after dropping the two bombs, America lied and said if Japan didn’t surrender, they would’ve dropped the bomb on Japan, the current site of the emperor. Basically pulling the biggest bluff in history. So I wanted to ask, which was true? Did they have a bomb or did they bluff Japan?
This sounds a bit confused. Without speculating as to the cause of your friend's confusion (it sounds like a garbled version of why Kokura wasn't bombed?), there was a third nuclear weapon in preparation, but its nuclear core was still in the United States when the Japanese finally indicated their desire for unconditional surrender, and it was never sent to Tinian, from which it would be assembled into the bomb and then possibly used. It had been ready to ship to Tinian around August 11th, but had been held up on the order of President Truman.
Around the same time Japan indicated it had accepted the terms of the Potsdam Declaration, there was momentum building in Washington DC for possibly shipping it out to Tinian and possibly using it on Tokyo (the target was never finalized, but there were some who thought Tokyo ought to be the next target), but it didn't happen, because Japan surrendered. The soonest they would have been able to use it would have been about 5 days after it was shipped, based on their previous experience in assembling the bomb and preparing the mission.
The US never claimed officially that Tokyo was a third target, but it wasn't a bluff that had the war continued, they would have likely dropped more. They were making all sorts of plans for producing more bombs, and starting to think about what they would do with the next ones (e.g., drop them on cities as soon as they were ready, or save them up and use a bunch at once, or use them in support of an invasion). The Manhattan Project production system could produce 3 plutonium bombs per month (the Nagasaki type bomb), and 1 uranium bomb (Hiroshima bomb) every 2 months, but they had plans in place to increase production if the war went on.
So it wasn't a bluff, but it also wasn't like your friend said, either. There is a lot of misinformation about this out there.