For future reference (since this is google's top answer ATM), to prevent jQuery UI from overriding bootstrap's or your custom style, you need to create a custom download and select the no-theme
theme. That will only include jQuery UI's resets, and not overload bootstrap's style for various elements.
While we're at it, some jQuery UI components (such as datepicker) have a native bootstrap implementation. The native bootstrap implementations will use the bootstrap css classes, attributes and layouts, so should have a better integration with the rest of the framework.