From my understanding, you have to be in the room when the map begins for them to count.

No you dont.

To elaborate more, you have to complete the map twice for it to count.

Actually, if you come to a map during an ongoing Bootcamp map, you would have to complete it twice to get 1 Bootcamp. If you were then when a map started, you only need to complete it once to get the Bootcamp. I don't know why, but I am guessing it is to stop people from farming Bootcamps so often.

It's exactly that, but OP said they did that.

I've been told that you need to enter before the mice respawn for it to count "the first time." Although typically you have to enter the hole twice for it to count, then all the times you enter the hole after that will count.
Bootcamp confuses me a bit, as I don't play too much in it.

That's untrue. There's nothing about respawning (I've never heard of this haha), it's just entering twice.