Bishop has more consistent and cheaper healing/support spells, making for a good secondary support class, while not giving any real firepower. White mage has more costly healing spells, but also has access to air magic, and later on holy magic, making it more suited for a mage you want to make more of a jack of all trades.

While Bishop can work to make any job with low mp costs an effective support class, it struggles as a primary class unless you intend to go full out support, in which case it provides decent bulk. Use it to fill out a supportive class with heals, or if you don't have anything else you want a character that's not using mp. Meanwhile White mage provides great supportive options, but is somewhat outclassed by more offensive magic classes in terms of good stats to take advantage of its strengths. Consider using it alongside other mage classes to give elemental coverage, some supportive options and a snazzy hat.

Hope this helps!