I had a druid character put together for a game. The game died shortly after it started, but the character build was sound. Transformation is definitely thaumaturgy. You have two basic options here:
You'd need either full Thaumaturgy, or you'd need Ritual in Biomancy, or in Transformation and Disruption, and you'd need "Mastery of" Biomancy or Transformation and Disruption to cast transformation at Evocation's Speed. You'd also need some serious Specializations and Focus in that area. Transforming with magic is difficult stuff and requires lots of shifts, which is why its so impressive when Listens to Wind does it. This is how Paranet Papers outlines transformations.
3 Shifts for an aspect to represent a new High Concept
2 Shifts for each point of refresh the powers you are adopting will cost
1 Shift in consequences for each point of refresh the powers you are adopting will cost (This should technically be an actual consequence taken by the target of your spell and is something that I require for transformation in my games (except when the person is transforming themselves or transforming in order to heal. I still require the shifts to be a part of the spell though, just no consequences taken). If you are transforming another person to give them super powers, they will need to take consequences to accept those powers or you will need to inflict those consequences on them. If they accept the consequences themselves, then you don't need to bring those shifts yourself, but if you are transforming someone against their will then those shifts are handled like an attack, so you add additional shifts to overcome their Endurance score and possible defense roll.)
In my games, [shifts needed to transform yourself] = 3+(3x[the refresh cost of the powers]).
Say you want to be a gorilla. You want Hulking Size and Supernatural Strength. That's 6 points of refresh. 3+3x6=21. That's 21 shifts to transform yourself into a gorilla. That is . . . a lot.
The other, more easily attainable option, mechanically speaking, is to simply take modular abilities and have that model your transformation magic, but that means that is the only kind of thaumaturgy you are likely to do. You wouldn't be able to do the rest magic offers without spending the refresh for it, and that becomes difficult at the normal levels of refresh. I kind of split the difference in my character.
My character,
Paul Williamson, externalized his transformations into a wolf companion named Voss. Follow the link to see his build.