# Sample Size when the sampling frame is small

I am sure this question has been answered, and may be obvious to those familiar with online surveys. But I am struggling with it.

I am surveying a specific population (local leaders in a specific state). We are doing an online survey, and will be basing the sample off of a contact list of approximately 3000 emails. I know the response rate is likely to be between 15 and 25%, and I know I want at least 300 complete surveys. This means I need to send the survey to at least 2000 people, which is 2/3 of my sampling frame. Obviously, the entire population (all the people that might be in local leadership roles across the state is somewhat of an "unknown" population)

Is this okay? It seems like a large portion of the sampling frame, and a lot of bias.

The contact list I am using came from an association that is relevant to this sector.

$$\text{FPC} = \sqrt{\frac{N-n}{N-1}}$$
which, if you get 300 responses becomes $\sqrt{\frac{270}{299}} = 0.95$