Re-opening this topic, because it does not seem possible to move items in bulk from one collection to another — the new bulk “Assign to collections” feature only copies items into the destination collections (with no ability to bulk remove the items from their original collections).
If I’m wrong about this, please demonstrate how to perform a bulk move. (@priya?)
If I’m not wrong I will also re-open the corresponding feature request.
Hi @grb! The “Assign to collections” action lets you both bulk add and remove items from collections. When you select “Assign to collections”, you’ll see which collections it’s currently assigned to under the “Select collections to assign” dropdown – you can remove collection assignments from there as well.
However, if you select items that are assigned across different collections, only the collections shared by all selected items will be shown. We’re exploring ways to improve how this is presented within the “Assign to collections” action.
Thanks for clarifying. So the point of confusion is that there actually is no “move” action, but that one can accomplish a “move” by performing two separate actions: 
remove from the original collection; 
add to the destination collection(s).
However, if items are selected from two different collections (e.g., using the “All Items” filter), then bulk assigning to a third collection will only copy the items — there does not seem to be a (bulk action) way of clearing the originally assigned collections in this scenario.