Given your description, its good to see the USAAF are clearly on the ball when it comes to security. If, say, all your B1s overflew the nutjob bowl then certain planners across the world might decide to act in a certain way. A random assortment leaves everyone guessing.
You could have a 9 plane fly-by of just B2s, and you’d still have less than half our operational stock committed (disregarding maintenance/readiness issues).
Using a few planes for a fly-by, particularly of anything other than B2, wouldn’t possibly “give away” any info.
B2s have made the trip from Whiteman AFB to perform flyovers at the past 20 or so Rose Bowls fwiw