How to determine create access for a given enitty and bundle
OK, I have figured it out. Here's what I am using to get access for the current user (in the createAccess() step the second parameter can be an account, if you need to pass an account):

// Before this, you need to get the entity type and bundle,
// shown here as $entity_type and $bundle .
$entity_manager = \Drupal::entityTypeManager();
$access_handler = $entity_manager-&gt;getAccessControlHandler($entity_type);
$access = FALSE;
if ($bundle) {
  $access = $access_handler-&gt;createAccess($bundle);
}
else {
  $access = $access_handler-&gt;createAccess();
}