The Pap smear involves no opening of the uterus and thus, according to most opinions, does not make a woman a niddah. Any subsequent bleeding found during the the next few days after the examination can be attributed to trauma to the cervix.
For medical reasons, a Pap smear cannot be scheduled while there is still uterine bleeding as this tends to make the interpretation of the test difficult.
From a halachic point of view, the best time to schedule a pap smear is after one has completed the shivah neki’im (seven blood-free days), and preferably after immersion in the mikveh. During this part of her cycle, a woman is halachically presumed not to be niddah. Therefore, any bleeding that may accompany the test is easier to attribute to the abrasion caused by the test (which does not make her a niddah) rather than to uterine bleeding (which might make her a niddah).
It is preferable not to do a Pap smear during the shivah neki’im, during which we are trying to establish that all uterine bleeding has ceased, particularly in the first three days. However, if for logistical reasons it must be scheduled during this time, you should ask a specific halachic question as to how to handle the situation.