A lot of it is about timing.
Just lightening the knots is better than attempting to bleach them to oblivion.
You need a hair lightening bleach (not a blonde dye) and you can get this in a packet or as individual products from somewhere like Sally's.
You want the activator/developer to be 40 vol.
Mix it up into a toothpaste consistency.
If you have a foam head stand, then wrap some plastic (clingfilm saranwrap) over it and then put a layer of bleach over the head.
Lay the system over the bleach and let it sit.
If you do it this way, its less likely for the bleach to travel up the shafts of the hairs.

Then keep an eye on it.
DON'T over bleach, thats when the knots get weakened and cause shedding.
Colour #1b is easier to bleach than a #1.

Rinse it, wash it thoroughly and then apply a knot sealer.

You should be good to go!