Two different liquids are enough. Let the density of these two liquids are ρ1, ρ2, respectively, with the bucket weighed mass of m1, m2, respectively, the mass of the bucket is m0, the volume of the bucket is V, you can get the system of equations.
Subtracting the two equations of the system of equations gives V. Substituting V into the first equation of the system of equations gives m0. see picture.