You're going swimming in robes?
Have you tried swimming with just pants on? It's hard. Less so when you have 2x that material all around you, rather than just on your legs. You'll be worse off than Phoenix, since she's just got the medieval version of shorty-shorts and some longboots. 'Course, she also can't swim, has a big ol' spear, and my junk, but I'm a collector and that stuff has value, so yeah.
Couldn't you just freeze its rear, and run the opposite direction, then use another spell to cast a cloud of sulfuric dust or something, to help mask your scent and allow you to run around. Combine that with an infinitely-farting spell on a tree, and the drake won't be able to hear, see, or smell you.