You can you have your own branches (along with a pull request) for bug fixes and features. Once the code review is complete you can merge your branches to master. You can use a plugin named git-reflow for making this process even simpler. After installing reflow, checkout to master and type git reflow start your-initials-branch-name which will create a new branch from master, this naming convention will help other to identify you branch very quickly.
Use can start working on you branch now, and after a commit you need to have a pull request, git reflow review master will open up a pull request against master with your current branch. Team members can review each others code and once they comment lgtm(Looks Good To Me) or :+1 (thumps up sign) you can merge your code to another branch(master is also a branch) using the command 'git reflow deliver master'. This will merge you local branch with master branch.