First you need to consider whether he had physical shape at all - otherwise he could have just 'drifted' across the mountains.
As we all know, he lost his shape at the end of the Second Age:
"...he forsook his body, and his spirit fled far away and hid in waste places; and he took no visible shape again for many long years."
Certainly he had a physical shape after Dol Gulder, since Gollum described his hand:
"He has only four on the Black Hand, but they are enough."
But what about the intervening period when the ring started to 'wake up' along with Sauron gaining in strength and power?
Tolkien's letters are slightly ambiguous on this point.
"...the year 1000 of the Third Age, when the shadow of Sauron began first to grow again to new shape." (Letter 144)
This does not necessarily mean a physical shape for Sauron's body at that time. Perhaps that was later once he had finally settled in Barad Dur.
"Sauron should be thought of as very terrible. The form that he took was that of a man of more than human stature, but not gigantic." (Letter 246)
Again, no timeline on this.
Also non-definitive is Gandalf in the Council Of Elrong:
"Some here will remember that many years ago I myself dared to pass the doors of the NEcromancer in Dol Guldur, and secretly explored his ways, and found thus that our fears were true: he was none other than Sauron, our Enemy of old, at length taking shape and power again."
Note that Gandalf says that Sauron is in the process of taking shape, not specifically saying that the task is completed.
So therefore I guess you have some artistic licence here, though if you assume he already had a physical shape whilst in Dol Gulder I doubt you can get away with saying he had enough power to shape-shift into a bat and simply fly home.