Considering that you are both adding a post and removing another one at the same time with each bump, I don't think it would affect your post count at all.
Let me give an example. I start with Post Count 0.
In Week 1 I post this:
1. Good post
2. Bump
3. Good post
Total paid: 2 posts.
Week 2, I start with Post Count 3.
4. Good post
5. Bump (I now delete my previous bump: Post Count is now 4 again, Post 4 becomes Post 3).
Total paid: 0 posts!
Out of 3 real posts one was not paid. My previous campaign manager solved this by checking post dates instead of post count.
I don't mind if some posts are missed once in a while, but I'd like to know how it's counted (I might bump less if it matters).