Well, we might start by asking who made the predictions. Would they not try to be involved in seeing if they are true? Science ia a belief system that exists to get around God the best way they know how. Their mandate is to constantly seek out new ways, when they get busted on the old ones over time! They brag about this even...
The prediction of a global genetic bottleneck is directly stated in Genesis, so long as you assume that God didn't go about creating more species or individuals afterward (which seems reasonable because otherwise taking them on the ark is pointless). A genetic bottleneck is by definition when the number of alleles is reduced drastically, and since an individual can only carry a certain number of genes a genetic bottleneck will be roughly equivalent to a population bottleneck. The genetic bottleneck will always be worse than the population bottleneck, because the population will probably contain some redundant copies of alleles, meaning the genes will be even more limited.
In my opinion, you are not going to win with this line or reasoning. You try to follow a bottleneck....how? What basic assumptions are made? Unless the evolving and genetics were the same then as they are now, that is a useless endeavor. If they were the same how did we live 1000 years?
Yes, some assumptions are made about mutation rate and generation time, which can't be directly observed but are expected to be the same. First, the genes must be read to determine a distribution and rate of variation in an allele. The mutation rate analysis will give a number of generations, and the generation time of current species is used to turn that number into a number of years. If you go by the Bible, I'm guessing you'd predict that any deviation from what is observed now would be toward longer lifespans and less mutation, right?
Reduced mutation rate will increase the number of generations required to explain variation, and a longer lifespan will mean the age calculated using current lifetime is an underestimate. Both these effects would mean the calculated bottleneck time would be even longer ago than calculated. Higher mutation rate and shorter generation times would have the opposite effect.
There's an additional measure of bottleneck, which is genetic drift. Genetic drift occurs in all populations but is by far more powerful in small populations. It is a result of the randomness of Mendelian genetics which you should have learned in school, and can cause alleles to be lost in a chance process because only a random half of an organism's alleles are passed on to each offspring. The final result is more commonly called inbreeding.
Both these processes are observed and accepted even by young earth creationists, and in any case are a mathematically necessary result of how we reproduce.
Now then, do you want to find whether the literal flood happened? If it did, where are all those genetic bottlenecks that must have resulted, and do they match the date of the flood?