Bears hotel
Doug - don't think twice: stay at the Hilton.
As you leave the main entrance, make a left and go about a half block to Balbo Drive. Cross Balbo and follow the hordes through Grant Park to Soldier Field. It's a nice walk.
I've had season tickets since 1976. I park near the Hilton and this is how I get to the stadium. (For games in colder weather, I change into my long underwear in the Hilton's mens room.)
Also, be aware that the Hilton bar is a meeting place for scores of Bear fans.
If you're somewhere else along the red line, exit at Roosevelt, but don't bother with a bus. It's an easy walk and you'll enjoy the camaraderie of the fans along the way.
I presume you're from Green Bay. If you're going to the Bear/Packer game, you won't be lonely. Thousands of Packer fans buy tickets from scalpers every year.