Hmm, cool physics!
Yeah, traditional audio amplifier circuits can be used to that end, with some optimization for the higher bandwidth. Audio only needs 20kHz, but to maintain low distortion, amps often roll off in the 100s kHz. A friend has bragged about his driver circuit delivering 7A to the output transistors in about the time you're looking at (and I forget exactly what that circuit looked like, but I don't think it was very special, just an elaboration on the usual design -- using cascode for the volt amp stage, and Darlingtons for the drivers).
These can be built with MOSFETs or BJTs; BJTs are somewhat easier to use, while MOSFETs need more drive voltage. In particular, a complementary source follower (as you suggested initially) needs an input voltage slightly beyond the supply rails in order to saturate. Or else for rail-to-rail inputs, the output saturates some amount -- a bit more than Vgs(th) -- away from either rail. (If you can afford AC coupling, this isn't so hard to deal with -- that is, using a capacitor to store the required additional voltage for a short period of time.)
You will need to pay attention to stray inductances. A mere 1cm of wire more than doubles the ESL in your circuit (figure ballpark 1nH/mm of wire or trace length, though it varies with geometry). Wide conductors, many in parallel, and nearby or interleaved grounds, are mandatory. I would hope that the transducer has a wide (stripline?) connection, or many alternating pins?
Your spec is blown with only, say,
L = V dt / dI
(48V) (0.5us) / (16A) = 1.5uH
so less than 1/10th of that will be desirable. 150nH isn't hard to achieve, but you can't be careless, and old school construction (like TO-3 devices on separate heatsinks with long wire leads) is definitely out. It certainly won't require RF construction techniques or devices; regular PC mount or SMT (TO-220, 247, D(2)PAK, etc.) will suffice.
Tim