No software is bug free (NASA's might be the closest) and all programmers try to not have bugs so remove that stuff.
I think your question is perhaps more "How do I manage a project without a Project Manager"
My answer to that is:
- Break stuff down into small tasks that you are very confident about estimating time for. This is key
- Focus on minimal functionality first - login, logout, visit home page, etc. before the real features.
- Use an Agile methodology.
- Talk to your client daily
- Use software that you, the client and programmer can share for tracking everything (features, bugs and Chores) such as Pivotal Tracker(which is my favorite), Trello, Jira or MS Project.
- Make sure you have a contract.