Here is a smartphone mount that lets you easily attach your iPhone to bicycle or bike handlebars. The Nite Ize Squeeze is a rotating handlebar mount with a clamp that fits most phones with or without a case (2.3 to 3.6-inches wide). It has a 360-degree rotating design, so you can use your phone in portrait or landscape orientation.
The Squeeze has grippy arms to keep your phone in place on bumpy roads. It comes with a mounting strap, so you can attach it to a stroller handle, grocery cart, golf cart, or wheelchair too. More information is available here.