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“After the lesson,” Snape snapped.

Under the pretext of holding up a measuring cup to see if he'd poured
out enough armadillo bile, Harry sneaked a sidelong glance at the pair
of them. Karkaroff looked extremely worried, and Snape looked angry.

Karkaroff hovered behind Snape's desk for the rest of the double
period. He seemed intent on preventing Snape from slipping away at the
end of class. Keen to hear what Karkaroff wanted to say, Harry
deliberately knocked over his bottle of armadillo bile with two
minutes to go to the bell, which gave him an excuse to duck down
behind his cauldron and mop up while the rest of the class moved
noisily toward the door.

The scene is in Snape's Potion class. I don't understand "with two
minutes to go to the bell". I think "the bell" is supposed to ring for the class dismissal here. But what does "go to the bell" mean? And "with two minutes" is confusing too. What does it mean exactly in this context?

-- Harry Potter and the Goblet of Fire

You are correct that the bell signifies the end of the class. However, the word "go" should not be joined with "to the bell"; rather you should read it as with "two minutes to go | to the bell". The phrase "to go" is a way of saying "the time that is left until something will happen". In this case the something is the bell ringing, and the time until it will happen is two minutes.

So putting this together, the phrase means "when there were two minutes left until the bell would ring". At that point Harry knocks over his bottle because that will give him an excuse to remain in the classroom even after the bell rings and everyone else leaves, which will enable him to eavesdrop on Snape and Karkaroff while they talk without realizing he is there.

I defer all major explanation to Alex's good answer. However, it may help your understanding to remember the other like and common expressions for this kind of temporal phrase:

two minutes to go till the bell

two minutes to go until the bell

two minutes to go before the bell

two minutes left / remaining till the bell

two minutes left / remaining until the bell

two minutes left / remaining before the bell

Keep in mind that, in this usage, "to go" is like an atomic word, a time signalling adjective whose usage us very like the time signalling adjective "ago" (as in "it happenned ten years ago").

That is, there are two things you can do with this temporal phrase to help understand it:

1. You can replace the second use of "to" in two minutes to go to the bell with a more precise, time-oriented preposition such as till, until or before.




2. You can replace the "to go" with the adjectives "left" (past participle of leave) or "remaining".

I suspect that what's confusing you is the different usages of "to" so near to one another.