The bonus seems to go up every 5 or 10 levels, same moment that you unlock a new picture on the card. But it's generally still a good habit to upgrade Slayer cards as soon as you have a wildcard available, otherwise you only risk forgetting about it when you do have your wilds at an increment of 5.
As for Slayer Cards for Shards: better to upgrade them anyway, since one or two of them will return in the next event after Shards as beta Slayers, just so you have them sorted out in advance and keep your wildcards sorted for future cards.