Firstly, there is a lot to be said for technique - using an "fingertips only" technique will only work for the cheapest silverware. Which part of the spoon/fork you try to bend also matters. You'll want to research and experiment with different techniques. Tine bends are easier than whole spoon bends. You can also start of by straightening out a metal paper clip and bending that if you want to practice the misdirection.
Regardless, strength does play a role and you want to get to a point where you can bend the toughest silverware with no visible effort. I can personally attest that the grip strengtheners used by strength atheletes/bodybuilders do work well. Get one with variable tension that you can dial in as you get stronger (early progress can be quick, so this will save you buying multiple times). I found more reps at lower intensity to yield better results for me for spoon bending purposes.
Remember the muscles worked are a bit different though, so this is a supplement to, not substitute for, practicing with actual spoons.