The ring bus is actually four rings, with the data ring being 32 bytes wide in each direction. It looks a lot like the ring in Larrabee, but Intel has not announced the width of that part yet. That said, it is 1024 bits wide, 512b times two directions. There are eight stops on the Becton ring, and data moves across it at one stop per clock.
To pull data off the ring, each stop can only pull one request off per clock. With two rings, this could be problematic if data comes in from both directions at the same time. The data flow would have to stop or the packets would have to go around again. Neither scenario is acceptable for a chip like this.
Intel solved this by putting some smarts into the ring stops, and added polarity to the rings. Each ring stop has a given polarity, odd or even, and can only pull from the correct ring that matches that polarity. The ring changes polarity once per clock, so which stop can read from which ring on a given cycle is easy to figure out.
Since a ring stop knows which other stop it is going to talk to, what the receiver polarity is, and what the hop count is between them, the sender can figure out when to send so that the receiver can actually read it. By delaying for a maximum of one cycle, a sender can assure the receiver can read it, and the case of two packets arriving at the same time never occurs.
In the end, the ring has four times the bandwidth of a similar width unidirectional ring, half the latency, and never sends anything that the receiver can't read. The raw bandwidth available is over 250GBps, and that scales nicely with the number of stops. You could safely speculate that Eagleton will have a 375GBps ring bus if the clocks don't change much.