Solo mining doesn't require any additional bandwidth, because the transactions you are trying to process into a block are the ones you are being sent notice of anyway. You don't have to receive anything you wouldn't receive otherwise, and you don't have to send anything unless you actually succeed in creating a valid block. The network doesn't even have to "send" your block reward---you put that transaction directly into the block you generate.
Pooled mining does require some additional bandwidth, because (1) the difficulty is artificially low, so the client submits "valid" hashes far more often, and (2) the server has to send updates to the clients as new transactions come in or new blocks are mined. Even then, there's no need for clients to send or receive more than a few tens of bytes per second on average---it's the servers that have to worry.