“Like Haman would not have noticed some random person not bowing”
According to the pesukim, it seems that Haman did not notice Mordechai not bowing until others brought it to his attention.
From the third perek:
? ??????????? ??????? ?????????, ??????-????????? ?????????–????????????: ???????? ?????? ??????, ??? ??????? ?????????. ? ???????, ????? (??????????) ?????? ???? ??????, ????? ??????, ????????; ???????????? ???????, ???????? ??????????? ???????? ??????????–????-??????? ?????, ??????-???? ????????. ? ???????? ?????–????-???? ??????????, ??????? ??????????????? ???; ??????????? ?????, ?????.