Well, with a Bigsby, you have to make sure the ball end of the string stays onto the little peg they give you, while you're also trying to hold the string in place so you can wind the tuning peg...takes three hands and it's a real pain, but it's doable.
With locking tuners, you just pull the string pretty tight (which keeps it on the peg), turn the tuner a bit (which locks the string down) and you're set.
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Place a piece of bath foam under the Bigby once you have fitted the string onto the pin, holds it in place and makes stringing a Bigsby a breeze.