The gemara says that a ger needs a beis din of 3, but isn't clear about what part of the conversion requires 3. Rashi seems to hold that both the tevila and to inform him of mitzvos requires 3. However, Tosafos proves from the gemara in yevamos that tevila can work even when done for other purposes such as to become tahor from keri, which is obviously not in the presence of 3. Based on this Tosafos holds that only kabalas hamitzvos absolutely requires a beis din of 3. The two answers of Tosafos seem to dispute whether the tevila would at least require 3 l'chatchila or not at all. The Shulchan Aruch (268:3) paskens like Tosafos (first answer) that tevila and mila require 3 l'chatchila, but b'dieved would work even if done in the presence of one. However, kabalas hamitzvos must be in the presence of 3. The Gr"a (15) points out that our gemara is a proof that without 3 the kabalas hamitzvos is absolutely invalid, because if it were only a l'chatchila requirement, it should be considered b'yado to convert. From the fact that we don't consider it b'yado implies that we always need 3 for some aspect of the geirus.
The rationale for kabalas hamitzvos requiring 3 more than the tevila, the shach and Taz quote from the Rosh, that kabalas hamitzvos is like techilas din which requires 3, but mila and tevila are like the g'mar din which can be done even at night and therefore would be more lenient. Based on this approach the dagul m'rvava explains that for a ger kattan where there isn't any kabalas hamitzvos, we would require a beis din of 3 for the tevila which is the primary act of conversion.
The Shulchan Aruch quotes that the opinion of Ri"f and Rambam is that even mila and tevila require 3 and are invalid if done not in the presence of 3.