You've been on the job for six weeks already... where has the time gone?!
I would suggest that instead of "ratting out" B, go to your nurse manager and pose a few questions such as "Who is supposed to cover the 30 min overlap between shifts? The person who I'm learning with is saying it's the next shift's job and I thought it was our job. What's the right thing to do?" Ask questions in that vein of things. Does this make sense? You really don't want to rat someone out, but it's really a shame that a person sat in their own excrement for an hour before someone got to them. I don't think that this is a person your facility wants to retain, however, you don't want to get the reputation of "tattling." It's a tough position to be in and I wish I had more concrete advice to give you.
Also, if there's another person who you think you'd train better with, say to your NM, "From watching [person c] I'm learning a lot more and I think we might be a better match. Is it possible you can change the assignment so I can work with him/her?"
I hope that everything else is going well with your job, and schooling, too!