What is the procedure of designing a salt bridge for a galvanic cell?
If you wish to do 25 trials with 5 trials per concentration, I would suggest the following:


You can use the same filter paper as long as the $\ce{Cu^{2+}}$ concentration remains constant. However, since you are changing the concentration 5 times, you will need 5 pieces of filter paper.
After every trial, thoroughly wash the filter paper with distilled water. 


So I would say you need at least 5 pieces, but you would not need to go all the way to 25 pieces. Just make sure to follow step 2 after each trial.