Here's a method I learned early on that will help you weave that bundle of wires together.
It's called "wire stacking". Basically, you just stack each wire on as you go. Start with the initial base wire and wrap the weaving wire around it 3 times to secure the wire. Then, weave in the next wire based on the pattern you're following. Continue adding base wires in until they have all been collected. (I'm weaving a triangle/zigzag weave to demonstrate this method). From there the weaving process gets much easier.
It's also a great way to bundle your wires without having to worry about damaging your wire or having to remove a sticky residue left by tape.