Jesus at Soul DeSaenz gives advice on using archival-quality pens to write in your Bible:
The biggest reason for using an archival quality pen is the ink, or rather the pigment. These pens use pigment ink rather [than] dye ink. Pigment ink is chemically stable, its pH is neutral, it is non-acidic and non-alkaline so it will not cause the paper to degrade over time. The pigment molecule is also larger than the dye molecule. It will outlast dye ink under extreme sun exposure… not that any of you will leave your Bible open for days at a time the next time you visit the Sahara but at least your notes will not fade. The larger pigment molecule is not just less susceptible to degradation it also helps in preventing bleeding or spreading which is a plus when you consider the thickness of most Bible paper. The pigment stays on the surface of the paper more than dye inks. The stability of the solvent used for the ink will prevent it from bleeding even if you wet the paper, it dries instantly so it is nearly impossible to smudge.
Jesus also gives specific recommendations for pens and explains how to match a pen’s nib width to Bible paper.