How do I bend or curve an object I created?

Brandon,

To add to what has already been said, whichever way you go, if you wish to keep the relative proportions (avoid stretching) you need to take more specific measures.

Just to add to what MohammadHarb and Myra Ferguson said, If you want type on this "banner," select both the type and the object and Group (Object > Group). Then add the Effect. Effect > Warp > Arc.

The same is true of Monica Gause's suggestion, if you want type as part of your Art Brush, Outline the Type (Type > Outline Type), group with the "banner," and drag into the Brushes panel to make an Artbrush.

Create a brush from it. Art brush with spacing by guides should offer you the possiblities you need.

You could use Effect > Warp > Arc... and adjust the amount of Bend in the Warp Options dialog.