"Where is this from?
The two parts relating to sleep ("sleep came in bits" and "dropped off") are straightforward. "In bits" means in small/short separate pieces, and we might imagine her repeatedly sleeping for short periods then waking up, perhaps 15 minutes at a time (although this is very much a guess). "Drop off" means fall asleep, as you will find in most dictionaries.
"Tore and darted" is figurative language, and here the author invites readers to imagine what is going on. Both verbs refer to rapid movement, perhaps short movements in different directions, but fast, and with an impression of suddenness. Clearly the night itself can do no such thing, not in a literal manner. Perhaps it refers to her thoughts, or perhaps it refers to insects in the air. Usually authors provide clues to figurative meanings in the way they create a scene, perhaps over several pages. When we only have a couple of sentences, we can only guess.