Animate the motion in a pre-comp, then bend it in place using distortion effects like Bezier Warp, Mesh Warp or Reshape.
Create your animated banner text layer. Make the layer 3D. Position the 3D text layer so that it lines up with the background image. Note that perspective is controlled by camera position not by focal length so move the layer away from he camera in Z and adjust the angle until it lines up with the background plate. Scale the layer to fit. Now position the anchor point of the layer where you want the bend to take place. Draw a mask around the text layer hiding the back half of the text layer. Duplicate the text layer and change the mask from add to subtract. Rotate the duplicate in Y until it goes around the corner. In this case it was easiest to use Centered paragraph style, start typing right on the corner of the box, create the first mask, duplicate the text layer, rotate the duplicate 90º to make the right angle, guess at about a 80 MM lens and add a camera, then adjust the Y position and X position first, then adjust the Z position to make the text line up with the edges of the box.
If you are talking about a different type of bending then show us a screen cap of the image you are using.