Wish I could say some Packer great in the 60s rode my bike, but you more-or-less had to live in Green Bay for that honor, since my mom would tell me I was nuts if I thought she was going to haul my bike to Green Bay in our Rambler sedan. I'm guessing todays mommas and poppas haul their kids' bikes on racks from all over the state to try and get a chance. I wouldn't be suprised if each Packer has the choice of 10 or more bikes each practice day.
The Packer practice fields are just across Oneida St. from the Lambeau Field parking lot, it's probably a couple block walk to the locker rooms and this was one of those traditions that just happened ... probably some kid offered his bike to a weary Packer player and offered to carry his helmet and pads.
There's actually a statute of a Packer riding a bike with a kid alongside somewhere in the Lambeau complex.