Are you saying a human today has more than 16 alleles or that if you take a thousand people and test the DNA, they would have a thousand different alleles between them?
Not a human. One human can never have more than two alleles and they may be duplicates of each other, so that one person may actually have two copies of the same allele.
Even thousands of different people may not have alleles that differ from one another; they may all have copies of the same allele.
But yes, there can be thousands of different alleles of the same gene in a large population. In any population the theoretical maximum of variations is twice the size of the population. But since most of the time we inherit unchanged copies of two of the alleles our parents had there are usually many copies of each allele in the population as a whole.
Is there a formula for how many would be needed in a bottleneck?
It says on the Wiki that "a great deal of genetic variation is hidden in the alleles."
As I said, the theoretical maximum for any population is twice the size of the population. Going in reverse, if you know the number of alleles in a population, you know the population cannot be more than half that number. In practice it would be well under half that number because most alleles have duplicate copies distributed among the population. Some more than other. So if a population has 10 alleles of one particular gene, it doesn't mean that each of them are found in 10% of the population. One may be found in 60% of the population, another in 20% and the rest in smaller numbers. (That is why, in humans, brown eyes are much, much more common than blue eyes--not only is the allele for brown eye colour dominant, there are just so many more alleles for brown pigment than for blue pigment.)
So if Noah had one allele for B type blood, his wife for A type blood and one of his sons wives for O type blood (and there are another dozen known genes that effect blood type activity) right there is all the variation for what we have today as far as blood type. Right?
No, because as you found out each allele is one of many that will produce the same blood-type.
So if Noah had A-type blood, we know he had one allele in the family of alleles that produce A-type blood. But since his time, where did the other alleles for A-type blood come from? Even if all eight of the family had alleles for A-type blood, at most there could be only 16 available for subsequent generations. And that is assuming that his sons all had mutations in their A-type alleles so that their A-type alleles were different from those of both their father and their mother. If there were no mutations in the inherited alleles, some had to be duplicated--reducing the number of alleles among the eight people. And if one or both of the alleles of Noah's wife were duplicates of Noah's, or any of the son's wives carried some duplicates of alleles found in their husbands, in-laws or each other--still less variation in the original gene pool.
This doesn't just apply to blood type. There are many genes which exist in dozens or hundreds of variant alleles. Both in humans and in other animals. (And the animals had only two flood survivors to start with--giving a maximum of four alleles for any one gene as a base starting-point.)
The only known method of increasing the number of alleles in a population is evolution. But that takes time and the time from the estimates of the date of the flood is just not enough to generate the observed variation from the restricted variation that could have survived the flood as described by creationists.