With the addition of the top right pop out for things like quests complete and invites to combat, I feel it would be appropriate to include this in the Bounty event.
Instead of a disrupting screen that announces a new enemy found, a red tab can pop in the top right that says new bounty and has the characters card with rank level on it. Tapping this would bring you to the bounty.
It’s kind of annoying to be quick running through tasks to have a big extra screen pop up that you have to click through to move on. This would be less intrusive.