Create bundles programmatically using ECK (Entity Construction Kit)
I just found a blog article here which gives an example on how to do exactly this:

After creating the entity type with the example code I gave in the question a bundle can be created as simply as this:

$entity_type_bundle = new Bundle();
$entity_type_bundle-&gt;name = 'eck_employee';
$entity_type_bundle-&gt;entity_type = 'eck_employee';
$entity_type_bundle-&gt;save();