I rode across the Heart of America bridge last month at 7:20 AM (Weekday) Going south you do not have a shoulder the first 200 feet or so going south on the west side of the road. Cars were civil and gave me no trouble.
Instead of crossing the exit lane at 3rd street I get off there and go over to Grand and south on Grand.
The light at the north end of the bridge is 10th street. You can take 10th to Atlantic first north/south street west of Burlington. Then go south on Atlantic to Harlem. I have had to wait for a train more often then not on my way to or from the airport.
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Enjoy the ride.
Bianchi Volpe 2006; Fuji Tahoe 1990