The correct option is
A needn't
The sentence indicates that the subject has bought a car and does not require to take the bus now. 'does not' indicates that the answer must be negative and also, the answer must indicate 'requirement'.
Option A is correct. In 'needn't', the word 'need' indicates 'requirement'. Also, 'needn't' is a negative word. Thus, it meets the required conditions and is correct.
Option B is incorrect. 'must' is a positive word and also, it indicates 'obligation' and not 'requirement'. Thus, it is incorrect.
Option C is incorrect. 'mustn't' is negative but, it indicates 'obligation' and not 'requirement'. Thus, it is incorrect.
Option D is incorrect. 'hadn't' is a form of auxiliary 'have'. 'have' can only be used with verbs in the past participle form to perfect tenses. Here, 'take' is not a past participle and thus, 'hadn't' will make the sentence grammatically incorrect.