There are many ways to do this. User Grb's answer is good but this method requires access to equipment.
If this is a highschool level project, you could make two Nutrient Agar petri plates. Spread 1 milliliter of unfiltered water on one and 1 milliliter of filtered water on the other. Make sure this is done in a sterile environment (Using a Bunsen burner for example). Growth of colonies on you filtered plate will tell you there are bacteria in the filtered water.
You can also count the number of colonies on both plates. If there are less colonies on the plate with filtered water, your filter works to a certain extent. If the counts are identical, your filter does not work. If you use colony counts, make sure you repeat the experiment multiple times for a more rigorous result.