Congrats to your offer at st. A. Are you on medical/oncology? I don't think they have a med surg department, which is why I'm asking. They have a separate surgical unit. Regardless, congrats.
In my search for apts, there were many nice places but they didn't have 1 bedroom, and only had 2 bedroom apts which I didn't want because they were more $. but i finally found a place for about 800 in Bismarck and it is a 1 bed 1 bath apartment with a garage. But I have to say that is hard to find a decent place less than 800-900 around here. I believe it's a little less pricey in Mandan which is about 15-20 min away from Bismarck and st. A.
I searched mostly using google, trulia, apartment guide, ndaa websites. I even resort to using craigslist to look for a place lol.
Bismarck is a nice city but it can be kind of "dry" as it doesn't have much fun activities. No nightclubs. But people here are nice, friendly, and helpful. I've met a few nurses from CA and who are also working on the med/onc unit so you won't be the only Cali nurse lol.
About the offer letter, you don't have to worry. When you get here and meet with HR for paperwork, you'll get an official letter inside the new hired packet.