A hadith is mainly verified from the chain of its narrators. Scholars, before deciding to either accept or reject any hadith, will spend time in studying the lives of all the narrators of the hadith. Aspects to be studied include the era in which the narrator lived - does it coincide with the era of the authority he is reporting on? Was the narrator old and learned enough to understand the hadith? Was the narrator a renowned fasiq (one who commits sins openly)? Has the narrator ever been known to fabricate a hadith?
Moreover, a hadith is also deemed accepted or rejected based on its contents. Do the contents of the hadith contradict the Holy Quran? Is the content of the hadith against logic?
There are many ahadith that have been acknowledged by all Muslims. Others have been accepted by all, but with differences in versions. Bukhari, in particular, is a Sunni scholar who compiled the ahadith, thus forming what we today know as the Sahih Bukhari. The fact is that we Shias do not reject Bukhari. There are many ahadith in Sahih Bukhari that have been accepted by Shias, but we Shias do not hold that whatever is in Sahih Bukhari is always true. For that reason, we also do not accept everything that is contained in Bihar-ul-Anwar, a book in which Allama Majlisi has compiled all the ahadith!
In conclusion, a hadith is accepted because of the authenticity of the narrators and the soundness of its content. Any doubts in the character and personality of any one narrator out of a chain of narrators will render the hadith unacceptable by Shia scholars.