From what I understand, the cost reduction effects from enchantments also effects staves. According to the UESP, the controlling school for the Staff of Magnus is both restoration and alteration.

So, my question is:

If I get 100% cost reduction in one school, will the staff have infinite charges? Or do I need 100% cost reduction in both schools?

As far as I know, staffs can never have infinite charges (without using a mod on PC). I think that 100% cost reduction means that it will basically double (or increase by 100%) the default number of charges that a staff has available before needing to be recharged.

Oh really? I've never been a mage but I'm trying to kit out a mage follower.

So do you need 100% cost reduction on both schools to double the charges?

That original assumption may be wrong. The player's skill level reduces the cost of each use of the staff, but it's not the same mechanism as the cost reduction for manually cast spells. Enchantments to fortify skill will boost the level used in the staff calculation, but the other numbers aren't the same, so 100% never happens.

I was planning on enchanting a bunch of alteration or restoration cost reduction gear for my follower so they could use the staff without me having to charge it all the time. Should I even bother? Does anyone know where I can find the actual math on this?

I've had Celann use the Staff of Magnus and I barely had to recharge it. I only did it when I check his inventory(once about every 2 irl hours to take out loot and put in more loot), and it was only down about a quarter. He used it all the time(mainly long dragon fights to siphon their breath) and he doesnt have high skills in Alteration or Restoration