Update 07/19/16: Today, the team updated Inbox as a response to one of the most requested features. Now users don't have to choose between Done or Delete. Both options are now available on the menu bar, without requiring users to choose and access a menu to perform the other task. This enhancement will be available on both mobile and web.
You will also notice the the option to choose what to do when finished with a message is gone from the settings page.
I know this is something you all have been hoping for and am excited to bring you the news.
Update 9/9/15: Empty Trash has now been added to iOs and should be available to everyone.
Update 8/3/15: Empty Trash has been added to the web version of Inbox by Gmail. Process is exactly the same as below for Android.
Today, it seems the Inbox team has started rolling out the ability to empty your trash from the Android App. This does not appear to have launched on the Web or iOs as of yet.
Now when you go into your trash folder you are presented with a message notifying you that items in trash delete automatically after 30 days, but you also have an option to EMPTY TRASH NOW.
So Deleters, rejoice - you got what you have all asked for. I am sure that Web and iOs will get this feature sometime in the future.
This feature will be an opt in feature, so when it rolls out, Mark as Done will be the default selection.
As always, with any Google feature rollout, this will rollout over time, and not everyone will have these features on day one.
Lots and lots of questions, posts and concerns about deleting in the new Inbox by GMail. I have just discovered that it is possible to delete to all from your bundles in one click. One caveat, you can only do these with the emails that are currently bundled in the Inbox. If they have been marked done or snoozed, this procedure will not effect them.
I know you are asking, come on already, how do we do this. It is simple. When you are in the Inbox, click on the bundle name. This will expand the bundle to show the emails that are currently in that bundle. Next click the three vertical dots to the right of the bundle name and you will see Move all to...Here you have multiple options: Trash, Spam, Remove from [Bundle Name]. Just select Trash and all your messages in that bundle will be sent to trash for permanent deletion in 30 days. Simple as that.
I personally have abandoned the deleting exercise since switching to Inbox, but I know many people are interested in this feature.