What are my chances at Bowdoin and Harvard?

Harvard is a very high reach, and, by next year, the acceptance rates, even for top below 10%qualified kids, will be even more abysmal. Acceptance rates at Bowdoin last year were under 10%, so it will be a high reach as well. However, as @merc81 wrote, applying ED will help your chances, and, in all honesty, your profile seems to match a LAC more than a large research university.

So Harvard - super high reach, Bowdoin, high reach/reach. As for every LAC, demonstrated interest goes a long way.

Now that you have two reaches, start finding your matches and your safety.

PS. would your family be able to afford Harvard, Bowdoin, or any other popular private college?