First off you're a great friend to care so much. A lot of people get weirded out by people who are sick, so kudos to you. I don't have MS but I have crohn's disease, which is a chronic incurable illness that has varying levels of impact on your life. So I hope I can shed some light on what it's like (at least for me) to deal with that. I think a lot of people who have a chronic illness worry that they're going to be a burden, and if you friend was pretty autonomous before she got MS, accepting the disease and the limitations it can cause is probably pretty hard. It's really difficult to go from I can do everything myself to asking for help. I know I'm stubborn about things, and probably border on stupid when it comes to admitting I may just need to slow down and not do everything.
You got great advice about discussing the MS with her. Don't force the discussion obviously, but for me anyway it's nice to have people ask me about crohn's. I don't usually go too in depth, but I appreciate the interest. Again, I always worry about if I'm being too graphic or talking about a depressing topic too much. So while we want to share our story with our friends, we worry that we might scare them/bore them/etc. You never want to turn into "that friend" that's always whining or asking for favors. Again, speaking from my experience here. Everyone's different.
Has she checked into support groups at all? Even an online discussion board can work wonders. If she's up to it of course. It's nice to be able to talk to other people who share the same illness and learn from them. Anyway, to sum it up you just being there for her is huge. She may get frustrated and try to not let you help, but understand it's nothing personal. Being open minded and flexible will help her understand you're not just there for a pity party that will eventually lapse, but you're just there to be her friend and help her when she needs it.
On an aside, I'm doing the MS150 in IL this year. I'll put in a few miles for your friend
"Only the meek get pinched, the bold survive"