What is the SAFEST way to get from Midway to O'Hare?

I will be flying in to Midway Airport in Chicago at 10pm. However, my hotel is near O'Hare Airport. I am a woman, and I'll be traveling by myself. What would be the SAFEST way to get to my hotel at O'Hare from Midway? Money is tight, so I'm not sure a cab will work.