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I set up a bundle containing Digital Downloads and got the attached error.
You need to install the digital downloads shipping module. Take a look at http://www.konakart.com/configurationfaq.php#How_can_i_configure_dig_down
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I tried this with Physical products as well and then also on the demo website and received the same error.
In our demo app the bundled products have been configured to give free shipping. Unfortunately we hadn't installed the free shipping module. It is fixed now.
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How should the Bundles be configured so that a Shipping Method is defined
They are treated the same way as any other product. Maybe with the above information, things are clearer now ?