This sheet is a good indicator how much time it takes to get to a certain artifact level.
The important milestones:
34 all traits
35 all traits and 5% heal/dmg
54 all traits and 15% heal/dmg
To add to that artifact levels also increase your HP and as a healer it also increases your dmg (till lvl 34). So the most important steps for pvp will be getting 35 traits because the first point in your 0/20 trait will give you flat 5% dmg / heal.
Getting to this point will take you around 100 days. Even if you bot 24/7 you will not be able to reduce this time by a lot (because of the importance of artifact knowledge).
Artifacts cap at level 34 in PvP. The 0/20 slot isn't active in it. Source, devs twatter.