I finally got the OAuth 2 approach working 
Here is the required setup (turns out, it’s somewhat simpler than Session OAuth):
STEP 1
Nothing required, you can leave this empty.
STEP 2
Copy this redirect URI provided by Zapier:
Create a third-party integration in your Bubble app.
- Paste the redirect URI provided by Zapier
- Define which page Bubble should use to authenticate the user if logged out
Your login page can be extremely simple, it just needs a login flow, nothing more (Bubble will handle the redirection since you provided the URI in the settings).
STEP 3
Paste your Client ID and Client Secret issued by Bubble at Step 2.
STEP 4
Fill out Bubble’s authorization URL (that one isn’t documented in Bubble’s reference at this time, it was provided to me by the support team).
Fill out Bubble’s access token request URL (this endpoint isn’t documented in Bubble’s reference either).
STEP 5
Set up your test with the following Authorization param in the Header, using a POST method:
Bearer {{bundle.authData.access_token}}
Note that your endpoint should NOT be able to run without authentication (that’s the point of the test).
You can return whatever data you want:
That’s it 