I will probably stir up a response, but I don't even pull credit in my market. I know that renters in my market have bad credit, that's why they aren't owners. I give my tenants an application, then verify the information they give me. If there is a lot of missing information (c'mon, you really forgot your kids names!?) or if I start finding bad information, I start getting nervous. I have a spot on the application for income, and I verify it afterward (I don't ask until after I have the application, just to make sure they tell the same story after I ask them to prove it).
I always call the current landlord, but REALLY like to talk to 2 landlords ago. The current landlord may have a reason to give a "good" reference, he/she may have a bad tenant to dispose of! With that said, 6 years at the same address says a lot if you read between the lines - she hasn't left and she hasn't been thrown out. Her rental is her HOME! She is more likely to respect your property as her own.
The other thing I like to look at is rent/income ratio, though you do also need to consider other living expenses. In your case, the nurse is at about 18%. If she has been at the same employer for a reasonable period, I would approve largely on that alone. Once you start approaching 30% of household income going to rent, you need to start being more careful. I do go higher than that, but my ears are on high alert for other "concerns". At 18%, unless she has other very large living expenses, she is well within the affordable range and is more likely to pay the heat bill on time and generally take care of her family and YOUR property.
Look at the car she is driving, does it go along with the story? If her car is modest (doesn't mean junk, just means not "flashy") and seems to be taken care of, that's a plus. If it is a luxury car and/or a model that doesn't seem appropriate for the stated income and her story, look closer at other information. I have had tenants go above and beyond for their car at the expense of my apartment!
Sometimes it boils down to a very unscientific "gut feeling". I had an applicant that I was very hesitant about. She was at the high end of my income/rent desired range, she had just left her husband (lot of drama in her story about that!), was moving in with a boyfriend and her daughter. While she filled out the application, I was chit-chatting with the daughter, she was 10 or 11 years old, and I found the daughter to be very respectful and quite the conversationalist. Had it not been for the conversation, I may not have approved the application. I did approve it and she has been one of my better tenants for over a year now. Another lesson/experience - if the kids are animals, they probably learned it from the parents. If the kids are decent, respectful, and seem to have good heads on their shoulders, they probably learned that from having parents with similar traits.
This was a rather lengthy response, and I could ramble on for another 20 minutes if you let me. Long story short, keeping in mind that I haven't seen the application or met the prospect, I would approve this in a second and not wait a week.
One final thought that may spark another topic - if you are unsure of your exit strategy on this property, your new nurse tenant might be an option. You might consider a creative financing arrangement and allow her an opportunity to buy the property from you over time. There are a number of ways to do that - new topic?
Best of luck