I understand that there is a way to increase blood shard caps that involves Greater Rifts, based on this tooltip
but how does it work?
41 Answer
The maximum increases the base amount (500) by 10 for each level in your Greater Rift solo personal best.
For example, if your very first solo Rift run was set to level 20 and successful (within the time limit), your base maximum (500) would increase by 20*10, for a new maximum of 700. You don't have to finish the levels one by one--it only counts your personal best solo Rift success.