The correct option is B As she was getting bored
An adverb clause is a group of words containing a subject and a verb,
and it functions as an adverb, by modifying an adjective, verb or an
adverb. Adverb clauses generally begin with a subordinate conjunction
(since, because, while, etc.).
Option A is correct because it is an
adverb clause of reason, 'as' is a conjunction that refers to cause or reason: "getting bored".
Option B is incorrect because it is a phrase, not an adverb clause.
Similarly, option C is incorrect because it is a phrase, not a clause.
Option D is incorrect because the answer lies in A.