I've been doing bug bounties for the past few years, here's some advice to get started:
1. Monitor https://hackerone.com, https://bugcrowd.com and Twitter for announcements of new programs.
2. When looking for bugs in sites with existing programs like Facebook your best chance is when they announce a new feature or product. This includes acquisitions (Facebook paid out over $100,000 for bugs when they added the Oculus websites to their program).