Finding security vulnerabilities in some of the most important software or website and give a warning message to the owner is known as Bug Bounty. A bug bounty program is conducted by different reputed website owner to reward to those who report bugs in their product, specially to those who pertaining to security exploits and vulnerabilities.
To became a Bug bounty, Don't jump directly to hacking.
You should have deep knowledge in the following topics:
1. Computer Fundamentals
You should know every things about computer fundamentals, how it works, all about input, processing, controlling, output, memory, bus system etc. A complete knowledge on computer architecture leads you towards a step forward in becoming Bug Bounty.
2. Internet(HTTP)
You should have deep knowledge about protocols. There is a way how the data in the Internet flows. What rules it flows and how the sender and receiver communicates with each other in Internet, everything you should know.
3. Networking (TCP/IP)
Internet is a part of Networking. Its a vast field. Everything in Networking field is important. You should have knowledge about OSI(Open Source Interconnection). You should know about the layers in Networking. You should have knowledge about the cables and devices.
4. Command Line Inteface(Shell)
You should have knowledge on Command line. You should have leave comfort zone to become a successful bug bounty. You don't have to work in GUI(Graphical User Interface) rather you must have knowledge on CUI(Command User Interface). There is a lot in command line interface to work in. You would not have drag and drop option there. CUI is very flexible and most of the tasks are done through it.
5. Linux
Linux is a most. You may be able to this through windows. But must of the web application are made in Linux. You should have knowledge in command used in Linux. Linux is open source operating system. You can download it from Internet for free. There is a very low risk of attack of viruses in Linux. If you have to penetrate in someone's operation system, then you should have a deep knowledge in Linux.
6. Web Technologies
Web technologies is a most for this task. If you have to taste your work in web then you should have knowledge of Web technologies. You should have knowledge of HTML and BackEnd programming like PHP, .net, JSP. And, the most important is, you should have knowledge of JavaScript. Today, almost all the web servers are using JavaScript and it has became backbone of server.
7. Programming Knowledge
You must have knowledge of programming languages. You should be a master of one of the programming Languages. Programming Languages like C , Java, Python etc are in trend and you should have knowledge on any of this programming languages. I suggest you learn Python.
If you have any doubt, let me know...