Sorry, I don’t have direct experience with PushBullet, but I should give it a try, so I can get notified when my dash battery is low. ":^)
Are you sending just JSON as your Hologram message (i.e. something like the messagebody above)?
So destination URL:
https://api.pushbullet.com/v2/pushes
Then in the route’s Payload (the decoded JSON):
<<decdata>>
Then down below the headers section add one for your authorization, not sure if you’d need to have the content-type/length.
Sending JSON from dash might look something like: