well done for a first attempt!
I still have problems with bubbles even after 4 years of making decorated cookies. always keep a toothpick handy to pop the bubbles. and let your icing stand for at least 30 minutes before using it to allow the bubbles to rise to the surface. cover it with saran wrap/cling film and a damp towel over the cling film to avoid crusting.
recently, I bought this wonderful tool that has helped me so much specially with the air bubbles. a heat gun! they're available at craft stores and mostly used for embossing, but can definitely be used for helping to dry the icing.
and here are some really wonderful blogs for cookie decorators, these blogs have a treasure load of info in them and are a big help: