The short answer is you'll likely have an easier time with cotton more suited to
vaping. Whether it has been bleached or not, well the cotton I got for vaping (forget where, or what, I have moved on UP to rayon these days, LOL) but it was slightly tan and in cut squares. I have a feeling it was one of the more popular options.
I know facial cotton was used in the beginning (with boiling) to reduce impurities/any traces of bleach (if they were there) so if that's what you got your hands on, and all you can get, you could probably use the search function to see how to handle them.
It may just be easier in the long run to get cotton "designed' or at least "marketed" so to speak for vaping for the cost of a little bit more. If this is all you have, you could probably use it with the caveat of making sure you know how to handle it.
With that said, I use Sally's Rayon Cellucotton and it's fine. It isn't organic, but it doesn't seem to contain any impurities and so really, what matters most (whatever you use) is that it's not full of impurities or horrible things. I very much doubt that you'll come to harm if you use the cotton you have on hand, (if you make sure to follow--whatever process I don't know much about because I was not around in the cotton ball days). But, I do believe it would be overall easier to just get some cotton designed for vaping, unless you simply can't (IDK your location and etc.)
Best of luck with whatever you wind up gong with.
Anna