I was wondering if I baked a cake, decorated it with all shortning buttercream icing- how long will it stay fresh? Would it need to be refridgerated? If refridgerated, will the colored icing bleed?

Most American b/c's are shelf stable, even when milk or cream are used as the liquid.

Sugar is hygroscopic, or moisture absorbing.
The powdered sugar in American b/c's controls the water activity in the butter/margarine and/or milk or cream in the mixture. (Butter and margarine are both 80% fat and 20% water, while shortening is 100% fat.)

Water activity & microbial growth:
(Prolonging Bakery Product Life.)

http://tinyurl.com/ya8po4z

WJ Scott in 1953 first established that it was water activity, not water content that correlated with bacterial growth:

http://tinyurl.com/bmsato

Formulating for increased shelf life:
(Decreasing water activity results in hostile environment for bacteria.)

http://tinyurl.com/csu2b9

Unless your filling is perishable, there's no need to refrigerate your cake.

Scratch cakes stale more quickly than mix cakes because they don't contain preservatives. Scratch cakes with little or no fat stale more quickly than scratch cakes that contain fat, and scratch cakes that contain little sugar will stale more quickly than scratch cakes that contain sugar.

HTH