They also only need one connection; they can simply split the data across all the workers. They will need to send shares from all the workers if they're not solo mining, but even those are less than 100 bytes each, and if that becomes too much of a nuisance they can just solo mine.
For an operation like this you'd need, at most, a couple of kilobytes per second. It runs as its own pool. Internally the traffic would be much higher.
Running a wallet with a full block chain would take more bandwidth.