"Я думала, не то что до дома, до кустов не добегу"
I thought to be unable to get (in time) not only to (my) home, but even to the (nearest) bushes. (Probably it means that the girl required WC super-urgently.)
добежать/добегать = до + бежать/бегать
It is a standard verb of motion "to run" with a standard prefix "до".
До + verb of motion = to get to (with specified way of motion in process of getting to).
Usually in vocabularies all combinations of verb with all standard prefixes are not listed because they are too many. Here, for example, the article about Russian prefixes.