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But the weight of the string isn't the force you need to pull.
Why not? If I try to pull a toy car alomg using a big thick rope, the weight of the rope is relevant, not just the weight of the toy car.
When you want to lift it up vertically, then the force that you need is exactly the same as the weight.
But when you push or pull it forward on a surface, you need a different force.
Push a golf ball on the table: you need very small force, much less than it's weight. Suck the same golf ball through a garden hose: you need much more force.
You want to look up "coefficient of friction" in your books.
The force of friction is dependent on its weight (or more specifically the force of normal) but not only its weight
It kind of is. That is still 11 tons of mass. To ring a bell, you need to create some velocity on the striker. Pull a 11 ton mass in a frictionless environment will result in an extremely slow rate of acceleration. But in the spirit of the post, I suspect they are not considering how hard they are ringing the bell.
You are technically right though. Even blowing on a string long enough and you could accelerate it up to speeds approaching that of light. Providing there is no friction.