Damage over Time for weapons?

Should I be using the damage over time purple gem for my weapons as a bleed barb? I don’t see any of my stats / %s change on the sheet when I socket them in and I assumed I should.

no, use green gems and take the passive at the end of the tree that allows bleeds to benefit from crit chance and damage. The reason why you won’t see any stat changes on the sheet when you slot these gems in is because the sheet only shows you generic, works 100% of the time crit damage, and the gems are conditional, as in, mobs have to be vulnerable for them to work.
EDIT: Unless you’re lower level and your crit chance is very low, then at that point the purple gems are probably more value