A coworker gave me a basket with some small potted plants. One of them is an ivy plant and I noticed it had several leaves covered in was appeared to be very fine spiderwebs. On closer examination, I saw that there were dozens of tiny white bugs moving along the 'webs'. What are these? They're about the size of a pen point, so I'm not able to see much detail.

Sounds like spider mites. Look them up for cures, but I think spraying with soap solution works.