Can I run bloomz-560m on a Mac with 128 GB?

Yes

Its published weights (1.12 GB) fit in the 96.0 GB a Mac with 128 GB can use, with room for an unknown amount of context.

hf download bigscience/bloomz-560m

Files and context on Mac with 128 GB

Each file of bloomz-560m (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

bloomz-560m on other hardware

Popular models that run on Mac with 128 GB

Assumes 75% of the Mac's memory is usable (macOS's default limit for the GPU; it can be raised) and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.