I think its kind of a given that a NB can come to a shower. its less than 2 months old, and your BFing. If someone says anything at the shower to you, I would find that very rude. If the baby was 5-6 months old, I would possibly rethink taking him, since i'm sure you'll already be in a schedule, ect.
If your still unsure, don't goto the MTB, its not her decision to have/not have kids there.. plus what happens if she says no? I would be upset at her. Ask whoevers hosting, and if they say absolutely not, then say, i'm sorry, but it's very unlikely I can come now, and I hope the MTB can understand.