Short Answer: While being concerned for Nance's wellbeing is important, the thing to remember is that you and Barb are not responsible for her or her financial security.
If you and Barb have been together for 4 years, it was no doubt obvious to Nance that one day you would want to live together. If she's training to be a doctor then she's no fool and wouldn't be oblivious to this fact.
Getting it straight between you and Barb
Firstly you need to make sure that you and Barb are absolutely on the same page on this. The last thing you both need as you take the big step of living together is to have a discord over Nance hanging over your heads.
Talking to Nance
When Barb talks to Nance, she should be straight with the facts. She should NOT be apologising for moving out; she simply should say something like:
Olynx and I have been together now for 4 years, and have decided to take the next step in our relationship. When the lease here ends, we will start living together. I understand that means that you may need to find another roommate, and it's important that Olynx and I take this step together for our relationship.
Most of all, you need to remember that neither you nor Barb have to justify this decision to Nance. You are not responsible for Nance, even though of course you are concerned for her financial future without Barb helping to pay the rent. You can offer to help her find another roommate, but again you aren't responsible for this either. You should however speak to her as soon as possible to give time for her to make other arrangements.
I know this sounds inflexible, but otherwise you are putting your relationship behind the needs of a third person. This is a bad idea for any relationship, so she needs to be firm that this is a decision that as an adult is hers to make, and as an adult it is Nance's to make alternative arrangements.