Have any friends in town? If they don't have data caps you could always beg an invite to their house with your PC and have it slurp down the game from there.
Just a quick google search shows people claiming 30-100MBps per hour of play. There's some things you can do to limit the usage - first, tell Steam that you're on dialup or the next level above dialup, and it will automatically adjust your data usage downwards. Second, disable the download of custom sprays, sounds, and maps (unfortunately, this will limit your server choice, but TF2 still has many active). Lastly, there are some console variables you can play with to tell the game to send/receive updates less frequently, they are rate, cl_updaterate, cl_cmdrate. Do some research on them, they'll affect your gameplay slightly.
Be careful when reading on the internet about speeds; a lot of people have no idea what the difference is between Kbps/Mbps and KB/s and MB/s, they use them interchangeably and they are not the same. Kbps and Mbps are kiloBITs/megaBITs per second (lower case 'b' = bit), and KB/s and MB/s are kiloBYTEs/megaBYTEs per second (upper case B = byte). Most 'speeds' are listed in Kbps/Mbps, and you need to convert that. There are 8 bits in a byte. So a lot of the napkin math I saw out there about this topic was hard to take credibly.
The most accurate sounding analysis I saw was:
For years, developers had to keep the plain old modem in mind with its 56Kbps bandwidth. Which means multiplayer communications were limited to that speed.
It's hasn't expanded much, a safe upper value today would be 100Kbps. That would be 12.5KBps, 750KB per minute, 45MB per hour or, at 120 hours, 5.4GB a month.
That's assuming 4 hours of play a day.