I think "brand new" would be stylistically more appropriate, and still carry the same meaning.
You're both correct, owlspotting and Sandybell, and Duo accepted "brand new," 10 April 2019. But, I wonder where this strange adjective phrase ("brand new") came from!
You'd need to write "Esta" before "es:"
"Esta es una bicicleta completamente nueva."
As in the previous example English speakers say or write, "It's a new bike". Completely is redundant.
There is nothing wrong with the statement in the context that if it was a broken, rusty contraption that somebody had rebuilt and made it look like a spanking new bike!!