What is a reasonable number of grad schools to apply to for a PhD in computer science?
However many schools you find that have academics that you want to work with.  

Research is like riding a bicycle.  You can obviously do it.  The application process for graduate school is mostly to vet applicants for those who can't ride the bicycle.  Therefore, the important next step for you is to find someone you will jive well with.  Applying to graduate schools should be more about that: find a professor that you'd be willing to enter into a serious personal relationship with. 

With that being said, I have friends who applied to 9, 3 schools in 3 tiers: "dream schools", "realistic schools", and "satisfactory schools".

I applied to one.  I found a professor I really liked and started an email correspondence with him 3 months before I even applied.  When applications came around, there wasn't a question of where I would apply or whether I would get in. 

Oh, and I'm a 4th year CS PhD candidate.