You start off stating that politics if off topic--then list a bunch of gov't agencies you infer to have the power to cover up any evidence...but you won't tolerate any politics!
Yes (although I'd qualify that statement by saying that it is most likely an institutional/industry secret, if you will, versus an absolute secret), assuming bigfoot exist and they are full-time biological entities.
How? Assuming (again!) that a human agency is responsible for the cover-up, a mix of normal cloak & dagger-type stuff mixed with a dependence on and a manipulation of the public's inherent apathy and disbelief.