The best way to solve this problem would be by starting with customizing Bootstrap using their customization tools.
http://getbootstrap.com/customize/
Go down to @headings-color and change it from "inherit" to something that you would like your headers to be across the site (if you like the default just change it to #333).
Note that this will keep all your headings the same color, as you requested.
Now in order to accomplish what you want that after you make this change you can now overwrite them specifically in your own CSS to apply your own color to them. The "inherit" keyword I always have found to be a pain in frameworks.