I need to replace the 10mm bolt that goes on the back of the alternator and attaches it to the bracket.
I think that makes it a GM 11515756 bolt, with m8x1.25x20mm dimensions.

Am I right? Do I need to order that part or will anything of those dimensions work?

U should be able to find a bolt to fit at the auto part store or if not the local hardware store will do. Ive got a bolt from a oreillys where i live a number of times & the hardware store a few times as well.. I will say tho its alot easier to take the Alt in with u to make it easier.. Most hardware stores wont even charge u for it. Theyll just wave u off ..

Couldn't agree with you more Shawn, more often times than not when I need to replace a fastener especially a bolt, I'll head to the hardware store. As long as you know the dimensions you'll do better at the hardware store. You can find grade 8 fasteners which will be stronger and certainly cheaper than what the dealer or parts store will sell you.

2004 Bonne SLE
1971 Chevelle SS