One witness to conversion - Igrot Moshe Yoreh Deah 3:112

Rav Moshe Feinstein was asked in 1974 about a conversion case where only one of the three members of the beit din actually saw the טבילה due to space constraints. Was this טבילה valid or did the woman need to go again in order to validate her conversion? Rav Moshe stated unequivocally that the conversion was valid, on a number of grounds:

1) Even though we say that one witness is not valid in the face of a חזקה, and in this case the חזקה would be that the woman is not Jewish, the fact is that in this case we say איתרע חזקתה - her חזקה is defective, due to the fact that she had accepted the mitzvot and made all of the many preparations for going to the mikveh and would not have gone through all of that if she was not planning on following through.

2) Tosafot in Gittin allow a witness to a גט to say בפני נכתב if he only heard the writing take place, even if he did not actually see it. In this case as well, if the people can say that they heard her dunk but did not see her, they can be accepted.

3) It could be that the beit din function not as witnesses but as judges. As such, they do not need to actually see her dip into the mikveh. It could be that there role is to instruct her to do so and may not even need to be present. This is based on Ramban, who writes that if the beit din instruct a person in mitzvot and the person accepts them and then the beit din instructs him to go and get a brit mila and go to the mikveh and he does so - even not in their presence - then his conversion is valid.

4) Even if they have to be present for the טבילה, it could be that their presence is ceremonial in nature (similar to their presence by סמיכה for פר העלם דבר של ציבור) and thus their not seeing the action does not invalidate the conversion.