Being the best player on either team doesn't really say much when you're in bronze. It means a lot in diamond and up, but in bronze it means almost nothing.
People have climbed out of bronze on their own ever since bronze was a thing, so if you're good enough to be a silver player you will get there.
In the meantime focus less on your team and more on what you can do to win games. Getting an S and still losing simply means you're not carrying enough weight just yet. Take on a role that can carry your team better or pick a champion that is good at winning outnumbered fights. Experiment with your runes, masteries, and items in normals to figure out what will best assist you with your climb.
Above all constantly practice your CSing. The more gold you get early the faster you can reach your late game power. Jump into a custom game with no runes or masteries and go to lane with no items. Last hit until the 10 minute mark and write down your CS. Set your goal at 100 and constantly push yourself to get closer and closer to it.
And make sure to abuse a lead. Don't just keep farming up and killing your lane opponents. Take down your tower and move to other objectives. Take dragon, take other towers, and just keep pushing until you've taken their nexus. If you're getting a lot of S ranks during losing games it means you didn't fully press your advantage that game. An S rank in a lost game simply means you could have won that game for your team, but you didn't.
Use that thought as motivation and you'll find a way to climb.