I hate to play the devil's advocate, but I think this is something that depends on the person.
If someone has been friends with someone that long, they tend to know what is typical of them and how they will deal with certain situations. My best friend seems to be a lot like you in that she is very budget-conscious. She doesn't want to lose money and in today's economy, I really don't blame anyone for that. Would I be offended if she asked me to sign a contract?
Probably not, because I know that would ease her mind, and knowing how she is, it wouldn't come as a huge surprise or offense because that's how she rolls.
That being said, it's hard to judge because I don't know either of you personally. If the issue is just with her, maybe you could make a contract with just her?
You know her best. How do you think she would react? Do you think she would be offended?