From quick searching it's not obvious how other tests do it, apart from calling Close on the dialog perhaps to achieve the same result? 

https://cs.chromium.org/search/?q=Close+dialog+file:browsertest&sq=package:chromium&type=cs

I think you'd better ask Trent.

I think you want BubbleFrameView::GetCloseButtonForTest()?

http://cs.chromium.org/BubbleFrameView::GetCloseButtonForTest

see e.g.

https://cs.chromium.org/chromium/src/chrome/browser/ui/views/translate/translate_bubble_view_unittest.cc?sq=package:chromium&l=227

I don't think we have one of those, unfortunately?

https://cs.chromium.org/chromium/src/chrome/browser/ui/views/autofill/save_card_bubble_views.h?l=32&rcl=bf54b51cf5f2546ecfb7ad6a880ebf45fddc02aa

SaveCardBubbleViews is a LocationBarBubbleDelegateView, which is a views::BubbleDialogDelegateView, which is a DialogDelegateView.

I *can* get the test to work by calling LocationBarBubbleDelegateView::CloseBubble().  However, that function is protected so I'm not allowed to call it from Browsertests...
https://cs.chromium.org/chromium/src/chrome/browser/ui/views/location_bar/location_bar_bubble_delegate_view.h?l=81&rcl=22bf150b6fad408e508eb0efcb1bd7938f2b451b
Could possibly override it in a different, friend-ed class and have that class call its super, but that seems like a less preferred approach.

see the second link I posted -  TranslateBubbleView is also a LocationBarBubbleDelegateView -- you just need to call GetBubbleFrameView on it. GetBubbleFrameView is protected, so you probably want to declare `SaveCardBubbleViewsFullFormBrowserTest` as a friend of SaveCardBubbleViews and add a static function to SaveCardBubbleViewsFullFormBrowserTest to close a bubble.

Ah, it is, sorry!  I tried looking for GetBubbleFrameView but it didn't show up because it was protected, yeah.  I'll give this a shot, thanks!

Thanks; this worked and is being resolved in https://chromium-review.googlesource.com/c/chromium/src/+/837155.  Closing bug.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/fbf6271cc126aad96d8a67d2e8677bc272f28a1c

commit fbf6271cc126aad96d8a67d2e8677bc272f28a1c
Author: Jared Saul <jsaul@google.com>
Date: Sat Jan 06 02:29:22 2018

Add browsertests for SendDetectedValues experiment

Bug:  789645 ,  791861 
Change-Id: I3bfa66427a58dd52c466a9dc9658c1830ebfa5e7
Reviewed-on: https://chromium-review.googlesource.com/837155
Commit-Queue: Jared Saul <jsaul@google.com>
Reviewed-by: Evan Stade <estade@chromium.org>
Cr-Commit-Position: refs/heads/master@{#527477}
[modify] https://crrev.com/fbf6271cc126aad96d8a67d2e8677bc272f28a1c/chrome/browser/ui/views/autofill/save_card_bubble_views.h
[modify] https://crrev.com/fbf6271cc126aad96d8a67d2e8677bc272f28a1c/chrome/browser/ui/views/autofill/save_card_bubble_views_browsertest.cc
[modify] https://crrev.com/fbf6271cc126aad96d8a67d2e8677bc272f28a1c/chrome/browser/ui/views/autofill/save_card_bubble_views_browsertest_base.cc
[modify] https://crrev.com/fbf6271cc126aad96d8a67d2e8677bc272f28a1c/chrome/browser/ui/views/autofill/save_card_bubble_views_browsertest_base.h
[modify] https://crrev.com/fbf6271cc126aad96d8a67d2e8677bc272f28a1c/components/test/data/autofill/credit_card_upload_form_address_and_cc.html