The bandwidth requirements are very low - you can sync time over a 56kbps serial port if you like.

However, the big benefit of PTP is having your precise timing and your main network connection share a single wire - so if your server needs 10 Gbps for whatever the server does, to get the highest accuracy you'd want a PTP compatible switch with 10Gbps ports.

The bandwidth is low, but the latency requirements are stringent since PTP does a wire delay calculation with multiple back-and-forth messages. If that gets affected by, for instance, jumbo frames being on, your bound on the clock value is much worse than if you have a relatively uncongested link.