If you're in the military, no public transport will ever be right, precisely because it's public.
But:
1) Mass transport isn't necessarily public. If there's a base with one town nearby where even just 20 of the people working on that base live, that's a good reason for a private bus.
2) Don't make the perfect the enemy of the good-enough. The military is even more of an edge case than emergency vehicles, and yet nobody seriously thinks normal people should get sirens and flashing lights on their commute to get past red lights. You get to keep whatever you need to do your job, because obviously you do.
But:
1) Mass transport isn't necessarily public. If there's a base with one town nearby where even just 20 of the people working on that base live, that's a good reason for a private bus.
2) Don't make the perfect the enemy of the good-enough. The military is even more of an edge case than emergency vehicles, and yet nobody seriously thinks normal people should get sirens and flashing lights on their commute to get past red lights. You get to keep whatever you need to do your job, because obviously you do.