Performance Monitoring is going to be your best bet. There is a whole category (in IIS7 and IIS6) called "Web Service". There are two counters of specific interest to you: "Web Service\Bytes Received/sec" and "Web Service\Bytes Sent/sec" sound like what you seek. You could also monitor FTP traffic as well (under the "FTP Service" category) or even raw TCP bandwidth. Check out this article for specifics (it is a little old, but still pertinent).
You can watch the values in real time, but I like to create a Data Collector to collect the data longitudinally over time. Here is a good read-me on setting up a Data Collector in Perfmon (assuming you are using 2008). I like to set Data Collectors to record in a CSV format running every 5 minutes. Open that in a few hours, and you'll have some great fun in Excel... averages, standard deviations, mins, maxes!
One side note: Be sure that your data center is talking in terms of Bytes, and not bits! Bandwidth is always discussed in bits. Oddly the Perfmon counters are in Bytes, so remember to adjust your math (1 byte = 8 bits) :-)