"what do you mean small no?? it's red!!
As long as you're courteous you can ride wherever you want!"
Sadly not legally true, though I have to admit to having cycled on the prom very very often. The Evening News columns and commenters would have you believe it's some sort of war zone, but as recombodna says, ride courteously and no-one bats an eyelid (certainly never have to me). I'll admit I only ride there knowing the police have stated that it's a sensible alternative and as long as you're careful they won't do you.
And red? Hell, most of the lanes in the city centre aren't red. And in Holyrood Park red actually signifies the pedestrian path, with the cycle lanes in green... ;)