So use Tor from someplace that won't be able to tell that you were one of a few people accessing Tor at that moment. Just go to a coffee shop or something.

Or presumably use a VPN to a server in another country, then hop on Tor. Any obvious problem with that?

Technically it'd be fine, there wouldn't be any direct evidence... but using a VPN on campus at the same time a bomb threat comes in through Tor could be enough to draw some suspicion. For something like this though I don't think they'd dig that deep.