No, there's no way to simple add the bootstrap styles to gwt components. You will have to deal with DOM, remove some GWT CSS classes and add GWT ones instead, and, at least you copy your code from one place to everywhere, you will made a class that extend the original component and use this new class everywhere, which is basically what GWT-Bootstrap do.
I know this because about one year ago, I wanted to do exactly what you're saying now: apply bootstrap styles to GWT components in a clean way, than, I managed it to work, and start the GWT-Bootstrap development.
GWT-Bootstrap actually already solved the most of the gwt+bootstrap integration bugs, and works well for basically any project. I know that some components are not implemented yet or have bugs, but, maybe you can fix some and made a pull-request, IMHO, that's better than rebuild all the things.