If you change to a bishop, your priest levels count toward learning priest spells. So you could learn level 5 priest spells at character level 11 (8 priest / 3 bishop), but you could learn level 5 mage/psionic/alchemist spells only at charecter level 19 (8 preist / 11 bishop).
Therefor, starting a bishop as another caster dosn't make much sense for me. The game would probably be over before you can cast the high-level spells at high power level (need to be level ~24 for that, or level ~32 with this class-change)

Intended to do this with my fighter-bishop duo. Wait for level 24 and high scool skills to be able to cast all spells in green at level 7, then switch to samurai for infinity helmet (and critical ability).

But i learned from other threads, and from own experience, that caster level plays a big part in damage and in overcoming resistances. And i wanted all my spells to grow in power, so i didn't switch (haven'd finished yet with them, might have some more fun at AP)

What I like to with my bishops is start them as an alchemist, mage or psioncist and then switch at level 2 to a bishop to jumpstart their skills.

I do this to get a jumps start with my magic skills (mage especially)
And to get Mythology skill (Alchemist) or Communication skill (Psionic)

I think I prefer one level as alchemist because they also get 11 throwing and sling and nice alchemy jumpstart (good for $$$ later)

Alchemists also start with a few more hit points, which bishops desperately need. Lvl 6&7 Alchemy spells are among the most powerful
there is so it works out nicely.

This is only dual classing I've found to be valuable.

GD