With a BB homozygote, what is the chance of a gamete having the B allele? The b allele?

With a BB homozygous the probability of a gamete having the B allele is 100%, and no chance of having the b allele.

Explanation:

For a given trait, B represents the dominant allele, while b is the recessive one. The fact that an individual has a homozygous (dominant) form for this trait means that their homologous chromosomes contain the B allele and, therefore, his gametes can only have the B allele.

In the case that the individual was heterozygous, the chances of having a gamete with B or b would be 50:50.

Learn more:

Homologous chromosomes with heterozygous or homozygous alleles link