I sometimes ask the same question. But probably we cannot find out about a new bounty immediately after its publication. Even websites like Bountiesalert.com or Bountyhive.io can't do that, either. Anyway, let's hope someone figure out the way and share with us.
I saved a link where you can find new bounties added on this forum. Kindly check this link:
https://docs.google.com/spreadsheets/d/1CiQRYU3JJyUnekC77DCG_7OgVUCeZy9l9KLaCaEwSik/edit#gid=0I'm not really sure if it is still active, it was created by tvplus006, credits to him.
As I have checked, the latest bounty added on the file was yesterday.